text:
Bayesian linear regression
From Wikipedia, the free encyclopedia
Jump to: navigation, search
It has been suggested that Bayesian multivariate linear regression be merged into this article. (Discuss) Proposed since March 2016.
Part of a series on Statistics
Bayesian statistics
Theory
Admissible decision rule
Bayesian efficiency
Bayesian probability
Probability interpretations
Bayes' theorem
Bayes' rule
Bayes factor
Bayesian inference
Bayesian network
Prior
Posterior
Likelihood
Conjugate prior
Posterior predictive
Hyperparameter
Hyperprior
Principle of indifference
Principle of maximum entropy
Empirical Bayes method
Cromwell's rule
Bernstein–von Mises theorem
Schwarz criterion
Credible interval
Maximum a posteriori estimation
Radical probabilism
Techniques
Bayesian linear regression
Bayesian estimator
Approximate Bayesian computation
Statistics portal
v
t
e
Part of a series on Statistics
Regression analysis
Models
Linear regression
Simple regression
Ordinary least squares
Polynomial regression
General linear model
Generalized linear model
Discrete choice
Logistic regression
Multinomial logit
Mixed logit
Probit
Multinomial probit
Ordered logit
Ordered probit
Poisson
Multilevel model
Fixed effects
Random effects
Mixed model
Nonlinear regression
Nonparametric
Semiparametric
Robust
Quantile
Isotonic
Principal components
Least angle
Local
Segmented
Errors-in-variables
Estimation
Least squares
Ordinary least squares
Linear (math)
Partial
Total
Generalized
Weighted
Non-linear
Non-negative
Iteratively reweighted
Ridge regression
Least absolute deviations
Bayesian
Bayesian multivariate
Background
Regression model validation
Mean and predicted response
Errors and residuals
Goodness of fit
Studentized residual
Gauss–Markov theorem
Statistics portal
v
t
e
In statistics, Bayesian linear regression is an approach to linear regression in which the statistical analysis is undertaken within the context of Bayesian inference. When the regression model has errors that have a normal distribution, and if a particular form of prior distribution is assumed, explicit results are available for the posterior probability distributions of the model's parameters.
Contents
[hide]
1 Model setup
2 With conjugate priors
2.1 Conjugate prior distribution
2.2 Posterior distribution
2.3 Model evidence
3 Other cases
4 See also
5 Notes
6 References
7 External links
8 Software
Model setup[edit]
Consider a standard linear regression problem, in which for i = 1 , . . . , n {\displaystyle i=1,...,n} we specify the conditional distribution of y i {\displaystyle y_{i}} given a k × 1 {\displaystyle k\times 1} predictor vector x i {\displaystyle \mathbf {x} _{i}} :
y i = x i T β + ϵ i , {\displaystyle y_{i}=\mathbf {x} _{i}^{\rm {T}}{\boldsymbol {\beta }}+\epsilon _{i},}
where β {\displaystyle {\boldsymbol {\beta }}} is a k × 1 {\displaystyle k\times 1} vector, and the ϵ i {\displaystyle \epsilon _{i}} are independent and identical normally distributed random variables:
ϵ i ∼ N ( 0 , σ 2 ) . {\displaystyle \epsilon _{i}\sim N(0,\sigma ^{2}).}
This corresponds to the following likelihood function:
ρ ( y | X , β , σ 2 ) ∝ ( σ 2 ) − n / 2 exp  ( − 1 2 σ 2 ( y − X β ) T ( y − X β ) ) . {\displaystyle \rho (\mathbf {y} |\mathbf {X} ,{\boldsymbol {\beta }},\sigma ^{2})\propto (\sigma ^{2})^{-n/2}\exp \left(-{\frac {1}{2{\sigma }^{2}}}(\mathbf {y} -\mathbf {X} {\boldsymbol {\beta }})^{\rm {T}}(\mathbf {y} -\mathbf {X} {\boldsymbol {\beta }})\right).}
The ordinary least squares solution is to estimate the coefficient vector using the Moore-Penrose pseudoinverse:
β ^ = ( X T X ) − 1 X T y {\displaystyle {\hat {\boldsymbol {\beta }}}=(\mathbf {X} ^{\rm {T}}\mathbf {X} )^{-1}\mathbf {X} ^{\rm {T}}\mathbf {y} }
where X {\displaystyle \mathbf {X} } is the n × k {\displaystyle n\times k} design matrix, each row of which is a predictor vector x i T {\displaystyle \mathbf {x} _{i}^{\rm {T}}} ; and y {\displaystyle \mathbf {y} } is the column n {\displaystyle n} -vector [ y 1 ⋯ y n ] T {\displaystyle [y_{1}\;\cdots \;y_{n}]^{\rm {T}}} .
This is a frequentist approach, and it assumes that there are enough measurements to say something meaningful about β {\displaystyle {\boldsymbol {\beta }}} . In the Bayesian approach, the data are supplemented with additional information in the form of a prior probability distribution. The prior belief about the parameters is combined with the data's likelihood function according to Bayes theorem to yield the posterior belief about the parameters β {\displaystyle {\boldsymbol {\beta }}} and σ {\displaystyle \sigma } . The prior can take different functional forms depending on the domain and the information that is available in a priori.
With conjugate priors[edit]
Conjugate prior distribution[edit]
For an arbitrary prior distribution, there may be no analytical solution for the posterior distribution. In this section, we will consider a so-called conjugate prior for which the posterior distribution can be derived analytically.
A prior ρ ( β , σ 2 ) {\displaystyle \rho ({\boldsymbol {\beta }},\sigma ^{2})} is conjugate to this likelihood function if it has the same functional form with respect to β {\displaystyle {\boldsymbol {\beta }}} and σ {\displaystyle \sigma } . Since the log-likelihood is quadratic in β {\displaystyle {\boldsymbol {\beta }}} , the log-likelihood is re-written such that the likelihood becomes normal in ( β − β ^ ) {\displaystyle ({\boldsymbol {\beta }}-{\hat {\boldsymbol {\beta }}})} . Write
( y − X β ) T ( y − X β ) = ( y − X β ^ ) T ( y − X β ^ ) + ( β − β ^ ) T ( X T X ) ( β − β ^ ) . {\displaystyle (\mathbf {y} -\mathbf {X} {\boldsymbol {\beta }})^{\rm {T}}(\mathbf {y} -\mathbf {X} {\boldsymbol {\beta }})=(\mathbf {y} -\mathbf {X} {\hat {\boldsymbol {\beta }}})^{\rm {T}}(\mathbf {y} -\mathbf {X} {\hat {\boldsymbol {\beta }}})+({\boldsymbol {\beta }}-{\hat {\boldsymbol {\beta }}})^{\rm {T}}(\mathbf {X} ^{\rm {T}}\mathbf {X} )({\boldsymbol {\beta }}-{\hat {\boldsymbol {\beta }}}).}
The likelihood is now re-written as
ρ ( y | X , β , σ 2 ) ∝ ( σ 2 ) − v 2 exp  ( − v s 2 2 σ 2 ) ( σ 2 ) − n − v 2 exp  ( − 1 2 σ 2 ( β − β ^ ) T ( X T X ) ( β − β ^ ) ) , {\displaystyle \rho (\mathbf {y} |\mathbf {X} ,{\boldsymbol {\beta }},\sigma ^{2})\propto (\sigma ^{2})^{-{\frac {v}{2}}}\exp \left(-{\frac {vs^{2}}{2{\sigma }^{2}}}\right)(\sigma ^{2})^{-{\frac {n-v}{2}}}\exp \left(-{\frac {1}{2{\sigma }^{2}}}({\boldsymbol {\beta }}-{\hat {\boldsymbol {\beta }}})^{\rm {T}}(\mathbf {X} ^{\rm {T}}\mathbf {X} )({\boldsymbol {\beta }}-{\hat {\boldsymbol {\beta }}})\right),}
where
v s 2 = ( y − X β ^ ) T ( y − X β ^ ) and v = n − k , {\displaystyle vs^{2}=(\mathbf {y} -\mathbf {X} {\hat {\boldsymbol {\beta }}})^{\rm {T}}(\mathbf {y} -\mathbf {X} {\hat {\boldsymbol {\beta }}})\quad {\text{ and }}\quad v=n-k,}
where k {\displaystyle k} is the number of regression coefficients.
This suggests a form for the prior:
ρ ( β , σ 2 ) = ρ ( σ 2 ) ρ ( β | σ 2 ) , {\displaystyle \rho ({\boldsymbol {\beta }},\sigma ^{2})=\rho (\sigma ^{2})\rho ({\boldsymbol {\beta }}|\sigma ^{2}),}
where ρ ( σ 2 ) {\displaystyle \rho (\sigma ^{2})} is an inverse-gamma distribution
ρ ( σ 2 ) ∝ ( σ 2 ) − v 0 2 − 1 exp  ( − v 0 s 0 2 2 σ 2 ) . {\displaystyle \rho (\sigma ^{2})\propto (\sigma ^{2})^{-{\frac {v_{0}}{2}}-1}\exp \left(-{\frac {v_{0}s_{0}^{2}}{2{\sigma }^{2}}}\right).}
In the notation introduced in the inverse-gamma distribution article, this is the density of an Inv-Gamma ( a 0 , b 0 ) {\displaystyle {\text{Inv-Gamma}}(a_{0},b_{0})} distribution with a 0 = v 0 2 {\displaystyle a_{0}={\tfrac {v_{0}}{2}}} and b 0 = 1 2 v 0 s 0 2 {\displaystyle b_{0}={\tfrac {1}{2}}v_{0}s_{0}^{2}} with v 0 {\displaystyle v_{0}} and s 0 2 {\displaystyle s_{0}^{2}} as the prior values of v {\displaystyle v} and s 2 {\displaystyle s^{2}} , respectively. Equivalently, it can also be described as a scaled inverse chi-squared distribution, Scale-inv- χ 2 ( v 0 , s 0 2 ) . {\displaystyle {\mbox{Scale-inv-}}\chi ^{2}(v_{0},s_{0}^{2}).}
Further the conditional prior density ρ ( β | σ 2 ) {\displaystyle \rho ({\boldsymbol {\beta }}|\sigma ^{2})} is a normal distribution,
ρ ( β | σ 2 ) ∝ ( σ 2 ) − k 2 exp  ( − 1 2 σ 2 ( β − μ 0 ) T Λ 0 ( β − μ 0 ) ) . {\displaystyle \rho ({\boldsymbol {\beta }}|\sigma ^{2})\propto (\sigma ^{2})^{-{\frac {k}{2}}}\exp \left(-{\frac {1}{2{\sigma }^{2}}}({\boldsymbol {\beta }}-{\boldsymbol {\mu }}_{0})^{\rm {T}}\mathbf {\Lambda } _{0}({\boldsymbol {\beta }}-{\boldsymbol {\mu }}_{0})\right).}
In the notation of the normal distribution, the conditional prior distribution is N ( μ 0 , σ 2 Λ 0 − 1 ) . {\displaystyle {\mathcal {N}}\left({\boldsymbol {\mu }}_{0},\sigma ^{2}\mathbf {\Lambda } _{0}^{-1}\right).}
Posterior distribution[edit]
With the prior now specified, the posterior distribution can be expressed as
ρ ( β , σ 2 | y , X ) ∝ ρ ( y | X , β , σ 2 ) ρ ( β | σ 2 ) ρ ( σ 2 ) ∝ ( σ 2 ) − n 2 exp  ( − 1 2 σ 2 ( y − X β ) T ( y − X β ) ) ( σ 2 ) − k 2 exp  ( − 1 2 σ 2 ( β − μ 0 ) T Λ 0 ( β − μ 0 ) ) ( σ 2 ) − ( a 0 + 1 ) exp  ( − b 0 σ 2 ) {\displaystyle {\begin{aligned}\rho ({\boldsymbol {\beta }},\sigma ^{2}|\mathbf {y} ,\mathbf {X} )&\propto \rho (\mathbf {y} |\mathbf {X} ,{\boldsymbol {\beta }},\sigma ^{2})\rho ({\boldsymbol {\beta }}|\sigma ^{2})\rho (\sigma ^{2})\\&\propto (\sigma ^{2})^{-{\frac {n}{2}}}\exp \left(-{\frac {1}{2{\sigma }^{2}}}(\mathbf {y} -\mathbf {X} {\boldsymbol {\beta }})^{\rm {T}}(\mathbf {y} -\mathbf {X} {\boldsymbol {\beta }})\right)(\sigma ^{2})^{-{\frac {k}{2}}}\exp \left(-{\frac {1}{2{\sigma }^{2}}}({\boldsymbol {\beta }}-{\boldsymbol {\mu }}_{0})^{\rm {T}}{\boldsymbol {\Lambda }}_{0}({\boldsymbol {\beta }}-{\boldsymbol {\mu }}_{0})\right)(\sigma ^{2})^{-(a_{0}+1)}\exp \left(-{\frac {b_{0}}{{\sigma }^{2}}}\right)\end{aligned}}}
With some re-arrangement,[1] the posterior can be re-written so that the posterior mean μ n {\displaystyle {\boldsymbol {\mu }}_{n}} of the parameter vector β {\displaystyle {\boldsymbol {\beta }}} can be expressed in terms of the least squares estimator β ^ {\displaystyle {\hat {\boldsymbol {\beta }}}} and the prior mean μ 0 {\displaystyle {\boldsymbol {\mu }}_{0}} , with the strength of the prior indicated by the prior precision matrix Λ 0 {\displaystyle {\boldsymbol {\Lambda }}_{0}}
μ n = ( X T X + Λ 0 ) − 1 ( X T X β ^ + Λ 0 μ 0 ) . {\displaystyle {\boldsymbol {\mu }}_{n}=(\mathbf {X} ^{\rm {T}}\mathbf {X} +{\boldsymbol {\Lambda }}_{0})^{-1}(\mathbf {X} ^{\rm {T}}\mathbf {X} {\hat {\boldsymbol {\beta }}}+{\boldsymbol {\Lambda }}_{0}{\boldsymbol {\mu }}_{0}).}
To justify that μ n {\displaystyle {\boldsymbol {\mu }}_{n}} is indeed the posterior mean, the quadratic terms in the exponential can be re-arranged as a quadratic form in β − μ n {\displaystyle {\boldsymbol {\beta }}-{\boldsymbol {\mu }}_{n}} .[2]
( y − X β ) T ( y − X β ) + ( β − μ 0 ) T Λ 0 ( β − μ 0 ) = ( β − μ n ) T ( X T X + Λ 0 ) ( β − μ n ) + y T y − μ n T ( X T X + Λ 0 ) μ n + μ 0 T Λ 0 μ 0 . {\displaystyle (\mathbf {y} -\mathbf {X} {\boldsymbol {\beta }})^{\rm {T}}(\mathbf {y} -\mathbf {X} {\boldsymbol {\beta }})+({\boldsymbol {\beta }}-{\boldsymbol {\mu }}_{0})^{\rm {T}}{\boldsymbol {\Lambda }}_{0}({\boldsymbol {\beta }}-{\boldsymbol {\mu }}_{0})=({\boldsymbol {\beta }}-{\boldsymbol {\mu }}_{n})^{\rm {T}}(\mathbf {X} ^{\rm {T}}\mathbf {X} +{\boldsymbol {\Lambda }}_{0})({\boldsymbol {\beta }}-{\boldsymbol {\mu }}_{n})+\mathbf {y} ^{\rm {T}}\mathbf {y} -{\boldsymbol {\mu }}_{n}^{\rm {T}}(\mathbf {X} ^{\rm {T}}\mathbf {X} +{\boldsymbol {\Lambda }}_{0}){\boldsymbol {\mu }}_{n}+{\boldsymbol {\mu }}_{0}^{\rm {T}}{\boldsymbol {\Lambda }}_{0}{\boldsymbol {\mu }}_{0}.}
Now the posterior can be expressed as a normal distribution times an inverse-gamma distribution:
ρ ( β , σ 2 | y , X ) ∝ ( σ 2 ) − k 2 exp  ( − 1 2 σ 2 ( β − μ n ) T ( X T X + Λ 0 ) ( β − μ n ) ) ( σ 2 ) − n + 2 a 0 2 − 1 exp  ( − 2 b 0 + y T y − μ n T ( X T X + Λ 0 ) μ n + μ 0 T Λ 0 μ 0 2 σ 2 ) . {\displaystyle \rho ({\boldsymbol {\beta }},\sigma ^{2}|\mathbf {y} ,\mathbf {X} )\propto (\sigma ^{2})^{-{\frac {k}{2}}}\exp \left(-{\frac {1}{2{\sigma }^{2}}}({\boldsymbol {\beta }}-{\boldsymbol {\mu }}_{n})^{\rm {T}}(\mathbf {X} ^{\rm {T}}\mathbf {X} +\mathbf {\Lambda } _{0})({\boldsymbol {\beta }}-{\boldsymbol {\mu }}_{n})\right)(\sigma ^{2})^{-{\frac {n+2a_{0}}{2}}-1}\exp \left(-{\frac {2b_{0}+\mathbf {y} ^{\rm {T}}\mathbf {y} -{\boldsymbol {\mu }}_{n}^{\rm {T}}(\mathbf {X} ^{\rm {T}}\mathbf {X} +{\boldsymbol {\Lambda }}_{0}){\boldsymbol {\mu }}_{n}+{\boldsymbol {\mu }}_{0}^{\rm {T}}{\boldsymbol {\Lambda }}_{0}{\boldsymbol {\mu }}_{0}}{2{\sigma }^{2}}}\right).}
Therefore, the posterior distribution can be parametrized as follows.
ρ ( β , σ 2 | y , X ) ∝ ρ ( β | σ 2 , y , X ) ρ ( σ 2 | y , X ) , {\displaystyle \rho ({\boldsymbol {\beta }},\sigma ^{2}|\mathbf {y} ,\mathbf {X} )\propto \rho ({\boldsymbol {\beta }}|\sigma ^{2},\mathbf {y} ,\mathbf {X} )\rho (\sigma ^{2}|\mathbf {y} ,\mathbf {X} ),}
where the two factors correspond to the densities of N ( μ n , σ 2 Λ n − 1 ) {\displaystyle {\mathcal {N}}\left({\boldsymbol {\mu }}_{n},\sigma ^{2}{\boldsymbol {\Lambda }}_{n}^{-1}\right)\,} and Inv-Gamma ( a n , b n ) {\displaystyle {\text{Inv-Gamma}}\left(a_{n},b_{n}\right)} distributions, with the parameters of these given by
Λ n = ( X T X + Λ 0 ) , μ n = ( Λ n ) − 1 ( X T X β ^ + Λ 0 μ 0 ) , {\displaystyle {\boldsymbol {\Lambda }}_{n}=(\mathbf {X} ^{\rm {T}}\mathbf {X} +\mathbf {\Lambda } _{0}),\quad {\boldsymbol {\mu }}_{n}=({\boldsymbol {\Lambda }}_{n})^{-1}(\mathbf {X} ^{\rm {T}}\mathbf {X} {\hat {\boldsymbol {\beta }}}+{\boldsymbol {\Lambda }}_{0}{\boldsymbol {\mu }}_{0}),}
a n = a 0 + n 2 , b n = b 0 + 1 2 ( y T y + μ 0 T Λ 0 μ 0 − μ n T Λ n μ n ) . {\displaystyle a_{n}=a_{0}+{\frac {n}{2}},\qquad b_{n}=b_{0}+{\frac {1}{2}}(\mathbf {y} ^{\rm {T}}\mathbf {y} +{\boldsymbol {\mu }}_{0}^{\rm {T}}{\boldsymbol {\Lambda }}_{0}{\boldsymbol {\mu }}_{0}-{\boldsymbol {\mu }}_{n}^{\rm {T}}{\boldsymbol {\Lambda }}_{n}{\boldsymbol {\mu }}_{n}).}
This can be interpreted as Bayesian learning where the parameters are updated according to the following equations.
μ n = ( X T X + Λ 0 ) − 1 ( Λ 0 μ 0 + X T X β ^ ) = ( X T X + Λ 0 ) − 1 ( Λ 0 μ 0 + X T y ) , {\displaystyle {\boldsymbol {\mu }}_{n}=(\mathbf {X} ^{\rm {T}}\mathbf {X} +{\boldsymbol {\Lambda }}_{0})^{-1}({\boldsymbol {\Lambda }}_{0}{\boldsymbol {\mu }}_{0}+\mathbf {X} ^{\rm {T}}\mathbf {X} {\hat {\boldsymbol {\beta }}})=(\mathbf {X} ^{\rm {T}}\mathbf {X} +{\boldsymbol {\Lambda }}_{0})^{-1}({\boldsymbol {\Lambda }}_{0}{\boldsymbol {\mu }}_{0}+\mathbf {X} ^{\rm {T}}\mathbf {y} ),}
Λ n = ( X T X + Λ 0 ) , {\displaystyle {\boldsymbol {\Lambda }}_{n}=(\mathbf {X} ^{\rm {T}}\mathbf {X} +{\boldsymbol {\Lambda }}_{0}),}
a n = a 0 + n 2 , {\displaystyle a_{n}=a_{0}+{\frac {n}{2}},}
b n = b 0 + 1 2 ( y T y + μ 0 T Λ 0 μ 0 − μ n T Λ n μ n ) . {\displaystyle b_{n}=b_{0}+{\frac {1}{2}}(\mathbf {y} ^{\rm {T}}\mathbf {y} +{\boldsymbol {\mu }}_{0}^{\rm {T}}{\boldsymbol {\Lambda }}_{0}{\boldsymbol {\mu }}_{0}-{\boldsymbol {\mu }}_{n}^{\rm {T}}{\boldsymbol {\Lambda }}_{n}{\boldsymbol {\mu }}_{n}).}
Model evidence[edit]
The model evidence p ( y | m ) {\displaystyle p(\mathbf {y} |m)} is the probability of the data given the model m {\displaystyle m} . It is also known as the marginal likelihood, and as the prior predictive density. Here, the model is defined by the likelihood function p ( y | X , β , σ ) {\displaystyle p(\mathbf {y} |\mathbf {X} ,{\boldsymbol {\beta }},\sigma )} and the prior distribution on the parameters, i.e. p ( β , σ ) {\displaystyle p({\boldsymbol {\beta }},\sigma )} . The model evidence captures in a single number how well such a model explains the observations. The model evidence of the Bayesian linear regression model presented in this section can be used to compare competing linear models by Bayesian model comparison. These models may differ in the number and values of the predictor variables as well as in their priors on the model parameters. Model complexity is already taken into account by the model evidence, because it marginalizes out the parameters by integrating p ( y , β , σ | X ) {\displaystyle p(\mathbf {y} ,{\boldsymbol {\beta }},\sigma |\mathbf {X} )} over all possible values of β {\displaystyle {\boldsymbol {\beta }}} and σ {\displaystyle \sigma } .
p ( y | m ) = ∫ p ( y | X , β , σ ) p ( β , σ ) d β d σ {\displaystyle p(\mathbf {y} |m)=\int p(\mathbf {y} |\mathbf {X} ,{\boldsymbol {\beta }},\sigma )\,p({\boldsymbol {\beta }},\sigma )\,d{\boldsymbol {\beta }}\,d\sigma }
This integral can be computed analytically and the solution is given in the following equation.[3]
p ( y | m ) = 1 ( 2 π ) n / 2 det ( Λ 0 ) det ( Λ n ) ⋅ b 0 a 0 b n a n ⋅ Γ ( a n ) Γ ( a 0 ) {\displaystyle p(\mathbf {y} |m)={\frac {1}{(2\pi )^{n/2}}}{\sqrt {\frac {\det({\boldsymbol {\Lambda }}_{0})}{\det({\boldsymbol {\Lambda }}_{n})}}}\cdot {\frac {b_{0}^{a_{0}}}{b_{n}^{a_{n}}}}\cdot {\frac {\Gamma (a_{n})}{\Gamma (a_{0})}}}
Here Γ {\displaystyle \Gamma } denotes the gamma function. Because we have chosen a conjugate prior, the marginal likelihood can also be easily computed by evaluating the following equality for arbitrary values of β {\displaystyle {\boldsymbol {\beta }}} and σ {\displaystyle \sigma } .
p ( y | m ) = p ( β , σ | m ) p ( y | X , β , σ , m ) p ( β , σ | y , X , m ) {\displaystyle p(\mathbf {y} |m)={\frac {p({\boldsymbol {\beta }},\sigma |m)\,p(\mathbf {y} |\mathbf {X} ,{\boldsymbol {\beta }},\sigma ,m)}{p({\boldsymbol {\beta }},\sigma |\mathbf {y} ,\mathbf {X} ,m)}}}
Note that this equation is nothing but a re-arrangement of Bayes theorem. Inserting the formulas for the prior, the likelihood, and the posterior and simplifying the resulting expression leads to the analytic expression given above.
Other cases[edit]
In general, it may be impossible or impractical to derive the posterior distribution analytically. However, it is possible to approximate the posterior by an approximate Bayesian inference method such as Monte Carlo sampling[4] or variational Bayes.
The special case μ 0 = 0 , Λ 0 = c I {\displaystyle {\boldsymbol {\mu }}_{0}=0,\mathbf {\Lambda } _{0}=c\mathbf {I} } is called ridge regression.
A similar analysis can be performed for the general case of the multivariate regression and part of this provides for Bayesian estimation of covariance matrices: see Bayesian multivariate linear regression.
See also[edit]
Bayes linear statistics
Tikhonov regularization
Spike and slab variable selection
This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. (August 2011) (Learn how and when to remove this template message)
Notes[edit]
Jump up ^ The intermediate steps of this computation can be found in O'Hagan (1994) at the beginning of the chapter on Linear models.
Jump up ^ The intermediate steps are in Fahrmeir et al. (2009) on page 188.
Jump up ^ The intermediate steps of this computation can be found in O'Hagan (1994) on page 257.
Jump up ^ Carlin and Louis(2008) and Gelman, et al. (2003) explain how to use sampling methods for Bayesian linear regression.
References[edit]
Box, G. E. P.; Tiao, G. C. (1973). Bayesian Inference in Statistical Analysis. Wiley. ISBN 0-471-57428-7.
Carlin, Bradley P. and Louis, Thomas A. (2008). Bayesian Methods for Data Analysis, Third Edition. Boca Raton, FL: Chapman and Hall/CRC. ISBN 1-58488-697-8. CS1 maint: Uses authors parameter (link)
Fahrmeir, L., Kneib, T., and Lang, S. (2009). Regression. Modelle, Methoden und Anwendungen (Second ed.). Heidelberg: Springer. ISBN 978-3-642-01836-7. doi:10.1007/978-3-642-01837-4. CS1 maint: Uses authors parameter (link)
Fornalski, Krzysztof W. (2015). "Applications of the robust Bayesian regression analysis". International Journal of Society Systems Science. 7 (4): 314–333. doi:10.1504/IJSSS.2015.073223.
Gelman, Andrew, Carlin, John B., Stern, Hal S. and Rubin, Donald B. (2003). Bayesian Data Analysis, Second Edition. Boca Raton, FL: Chapman and Hall/CRC. ISBN 1-58488-388-X. CS1 maint: Uses authors parameter (link)
Goldstein, Michael; Wooff, David (2007). Bayes Linear Statistics, Theory & Methods. Wiley. ISBN 978-0-470-01562-9.
Minka, Thomas P. (2001) Bayesian Linear Regression, Microsoft research web page
Rossi, Peter E.; Allenby, Greg M.; McCulloch, Robert (2006). Bayesian Statistics and Marketing. John Wiley & Sons. ISBN 0470863676.
O'Hagan, Anthony (1994). Bayesian Inference. Kendall's Advanced Theory of Statistics. 2B (First ed.). Halsted. ISBN 0-340-52922-9. CS1 maint: Uses authors parameter (link)
Sivia, D.S., Skilling, J. (2006). Data Analysis - A Bayesian Tutorial (Second ed.). Oxford University Press. CS1 maint: Uses authors parameter (link)
Walter, Gero; Augustin, Thomas (2009). "Bayesian Linear Regression—Different Conjugate Models and Their (In)Sensitivity to Prior-Data Conflict" (PDF). Technical Report Number 069, Department of Statistics, University of Munich.
External links[edit]
Bayesian estimation of linear models (R programming wikibook). Bayesian linear regression as implemented in R.
Software[edit]
python
Bayesian Type-II Linear Regression code, tutorial
ARD Linear Regression code
ARD Linear Regression with kernelized features code, tutorial
[show]
v
t
e
Least squares and regression analysis
Computational statistics
Least squares
Linear least squares
Non-linear least squares
Iteratively reweighted least squares
Correlation and dependence
Pearson product-moment correlation
Rank correlation (Spearman's rho
Kendall's tau)
Partial correlation
Confounding variable
Regression analysis
Ordinary least squares
Partial least squares
Total least squares
Ridge regression
Regression as a
statistical model
Linear regression
Simple linear regression
Ordinary least squares
Generalized least squares
Weighted least squares
General linear model
Predictor structure
Polynomial regression
Growth curve (statistics)
Segmented regression
Local regression
Non-standard
Nonlinear regression
Nonparametric
Semiparametric
Robust
Quantile
Isotonic
Non-normal errors
Generalized linear model
Binomial
Poisson
Logistic
Decomposition of variance
Analysis of variance
Analysis of covariance
Multivariate AOV
Model exploration
Mallows's Cp
Stepwise regression
Model selection
Regression model validation
Background
Mean and predicted response
Gauss–Markov theorem
Errors and residuals
Goodness of fit
Studentized residual
Minimum mean-square error
Design of experiments
Response surface methodology
Optimal design
Bayesian design
Numerical approximation
Numerical analysis
Approximation theory
Numerical integration
Gaussian quadrature
Orthogonal polynomials
Chebyshev polynomials
Chebyshev nodes
Applications
Curve fitting
Calibration curve
Numerical smoothing and differentiation
System identification
Moving least squares
Regression analysis category
Statistics category
Statistics portal
Statistics outline
Statistics topics
[hide]
v
t
e
Statistics
Outline
Index
[show]
Descriptive statistics
Continuous data
Center
Mean
arithmetic
geometric
harmonic
Median
Mode
Dispersion
Variance
Standard deviation
Coefficient of variation
Percentile
Range
Interquartile range
Shape
Central limit theorem
Moments
Skewness
Kurtosis
L-moments
Count data
Index of dispersion
Summary tables
Grouped data
Frequency distribution
Contingency table
Dependence
Pearson product-moment correlation
Rank correlation
Spearman's rho
Kendall's tau
Partial correlation
Scatter plot
Graphics
Bar chart
Biplot
Box plot
Control chart
Correlogram
Fan chart
Forest plot
Histogram
Pie chart
Q–Q plot
Run chart
Scatter plot
Stem-and-leaf display
Radar chart
[show]
Data collection
Study design
Population
Statistic
Effect size
Statistical power
Sample size determination
Missing data
Survey methodology
Sampling
stratified
cluster
Standard error
Opinion poll
Questionnaire
Controlled experiments
Design
control
optimal
Controlled trial
Randomized
Random assignment
Replication
Blocking
Interaction
Factorial experiment
Uncontrolled studies
Observational study
Natural experiment
Quasi-experiment
[show]
Statistical inference
Statistical theory
Population
Statistic
Probability distribution
Sampling distribution
Order statistic
Empirical distribution
Density estimation
Statistical model
Lp space
Parameter
location
scale
shape
Parametric family
Likelihood (monotone)
Location–scale family
Exponential family
Completeness
Sufficiency
Statistical functional
Bootstrap
U
V
Optimal decision
loss function
Efficiency
Statistical distance
divergence
Asymptotics
Robustness
Frequentist inference
Point estimation
Estimating equations
Maximum likelihood
Method of moments
M-estimator
Minimum distance
Unbiased estimators
Mean-unbiased minimum-variance
Rao–Blackwellization
Lehmann–Scheffé theorem
Median unbiased
Plug-in
Interval estimation
Confidence interval
Pivot
Likelihood interval
Prediction interval
Tolerance interval
Resampling
Bootstrap
Jackknife
Testing hypotheses
1- & 2-tails
Power
Uniformly most powerful test
Permutation test
Randomization test
Multiple comparisons
Parametric tests
Likelihood-ratio
Wald
Score
Specific tests
Z (normal)
Student's t-test
F
Goodness of fit
Chi-squared
Kolmogorov–Smirnov
Anderson–Darling
Lilliefors
Jarque–Bera
Normality (Shapiro–Wilk)
Likelihood-ratio test
Model selection
Cross validation
AIC
BIC
Rank statistics
Sign
Sample median
Signed rank (Wilcoxon)
Hodges–Lehmann estimator
Rank sum (Mann–Whitney)
Nonparametric anova
1-way (Kruskal–Wallis)
2-way (Friedman)
Ordered alternative (Jonckheere–Terpstra)
Bayesian inference
Bayesian probability
prior
posterior
Credible interval
Bayes factor
Bayesian estimator
Maximum posterior estimator
[hide]
Correlation
Regression analysis
Correlation
Pearson product-moment
Partial correlation
Confounding variable
Coefficient of determination
Regression analysis
Errors and residuals
Regression model validation
Mixed effects models
Simultaneous equations models
Multivariate adaptive regression splines (MARS)
Linear regression
Simple linear regression
Ordinary least squares
General linear model
Bayesian regression
Non-standard predictors
Nonlinear regression
Nonparametric
Semiparametric
Isotonic
Robust
Heteroscedasticity
Homoscedasticity
Generalized linear model
Exponential families
Logistic (Bernoulli) / Binomial / Poisson regressions
Partition of variance
Analysis of variance (ANOVA, anova)
Analysis of covariance
Multivariate ANOVA
Degrees of freedom
[show]
Categorical / Multivariate / Time-series / Survival analysis
Categorical
Cohen's kappa
Contingency table
Graphical model
Log-linear model
McNemar's test
Multivariate
Regression
Manova
Principal components
Canonical correlation
Discriminant analysis
Cluster analysis
Classification
Structural equation model
Factor analysis
Multivariate distributions
Elliptical distributions
Normal
Time-series
General
Decomposition
Trend
Stationarity
Seasonal adjustment
Exponential smoothing
Cointegration
Structural break
Granger causality
Specific tests
Dickey–Fuller
Johansen
Q-statistic (Ljung–Box)
Durbin–Watson
Breusch–Godfrey
Time domain
Autocorrelation (ACF)
partial (PACF)
Cross-correlation (XCF)
ARMA model
ARIMA model (Box–Jenkins)
Autoregressive conditional heteroskedasticity (ARCH)
Vector autoregression (VAR)
Frequency domain
Spectral density estimation
Fourier analysis
Wavelet
Survival
Survival function
Kaplan–Meier estimator (product limit)
Proportional hazards models
Accelerated failure time (AFT) model
First hitting time
Hazard function
Nelson–Aalen estimator
Test
Log-rank test
[show]
Applications
Biostatistics
Bioinformatics
Clinical trials / studies
Epidemiology
Medical statistics
Engineering statistics
Chemometrics
Methods engineering
Probabilistic design
Process / quality control
Reliability
System identification
Social statistics
Actuarial science
Census
Crime statistics
Demography
Econometrics
National accounts
Official statistics
Population statistics
Psychometrics
Spatial statistics
Cartography
Environmental statistics
Geographic information system
Geostatistics
Kriging
Category
Portal
Commons
WikiProject
Retrieved from "https://en.wikipedia.org/w/index.php?title=Bayesian_linear_regression&oldid=804607651"
Categories:
Bayesian inference
Single-equation methods (econometrics)
Hidden categories:
Articles to be merged from March 2016
All articles to be merged
Articles lacking in-text citations from August 2011
All articles lacking in-text citations
CS1 maint: Uses authors parameter
Navigation menu
Personal tools
Not logged in
Talk
Contributions
Create account
Log in
Namespaces
Article
Talk
Variants
Views
Read
Edit
View history
More
Search
Navigation
Main page
Contents
Featured content
Current events
Random article
Donate to Wikipedia
Wikipedia store
Interaction
Help
About Wikipedia
Community portal
Recent changes
Contact page
Tools
What links here
Related changes
Upload file
Special pages
Permanent link
Page information
Wikidata item
Cite this page
Print/export
Create a book
Download as PDF
Printable version
Languages
Українська
Edit links
This page was last edited on 10 October 2017, at 02:32.
Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.
Privacy policy
About Wikipedia
Disclaimers
Contact Wikipedia
Developers
Cookie statement
Mobile view
Enable previews

values: mw-page-base noprint

values: mw-head-base noprint

values: firstHeading firstHeading en

values: siteSub noprint

values: jump-to-nav mw-jump

value: tbody

value: table

attrs: class role

values:
plainlinks metadata ambox ambox-move
presentation

values:
/wiki/Bayes%27_rule
mw-redirect
Bayes' rule

values:
/wiki/Schwarz_criterion
mw-redirect
Schwarz criterion

values:
/wiki/Bayesian_estimator
mw-redirect
Bayesian estimator

values: float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;background:#f9f9f9;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%

values:
/wiki/Multinomial_logit
mw-redirect
Multinomial logit

values:
/wiki/Weighted_least_squares
mw-redirect
Weighted least squares

values:
/wiki/Regression_model_validation
mw-redirect
Regression model validation

values:
/wiki/Prior_distribution
mw-redirect
Prior distribution

values: vertical-align: -0.671ex; width:11.722ex; height:2.509ex;

values: vertical-align: -0.671ex; width:1.957ex; height:2.009ex;

values: vertical-align: -0.338ex; width:5.245ex; height:2.176ex;

values: vertical-align: -0.671ex; width:2.228ex; height:2.009ex;

values: vertical-align: -1.005ex; width:14.728ex; height:3.176ex;

values: y_{i} = \mathbf{x}_{i}^{\rm T} \boldsymbol\beta  + \epsilon_{i},

values: vertical-align: -0.671ex; width:1.545ex; height:2.509ex;

values: vertical-align: -0.671ex; width:1.762ex; height:2.009ex;

values:
/wiki/Normally_distributed
mw-redirect
Normally distributed

values: vertical-align: -0.838ex; width:14.052ex; height:3.176ex;

values: vertical-align: -2.505ex; width:59.78ex; height:6.176ex;

values: \rho(\mathbf{y}|\mathbf{X},\boldsymbol\beta,\sigma^{2}) \propto (\sigma^{2})^{-n/2} \exp\left(-\frac{1}{2{\sigma}^{2}}(\mathbf{y}- \mathbf{X} \boldsymbol\beta)^{\rm T}(\mathbf{y}- \mathbf{X} \boldsymbol\beta)\right).

values:
/wiki/Moore-Penrose_pseudoinverse
mw-redirect
Moore-Penrose pseudoinverse

values: vertical-align: -0.838ex; width:19.232ex; height:3.343ex;

values: \hat{\boldsymbol\beta} = (\mathbf{X}^{\rm T}\mathbf{X})^{-1}\mathbf{X}^{\rm T}\mathbf{y}

values: vertical-align: -0.338ex; width:2.03ex; height:2.176ex;

values: vertical-align: -0.338ex; width:5.478ex; height:2.176ex;

values: vertical-align: -1.005ex; width:2.848ex; height:3.176ex;

values: vertical-align: -0.671ex; width:1.421ex; height:2.009ex;

values: vertical-align: -0.338ex; width:1.405ex; height:1.676ex;

values: vertical-align: -0.838ex; width:12.126ex; height:3.176ex;

values:
/wiki/Prior_probability_distribution
mw-redirect
Prior probability distribution

values:
/wiki/Bayes_theorem
mw-redirect
Bayes theorem

values: vertical-align: -0.338ex; width:1.34ex; height:1.676ex;

values: Edit section: Conjugate prior distribution

values:
/wiki/Posterior_distribution
mw-redirect
Posterior distribution

values: vertical-align: -0.838ex; width:8.034ex; height:3.176ex;

values: vertical-align: -0.838ex; width:7.807ex; height:3.343ex;

values: vertical-align: -0.838ex; width:72.607ex; height:3.343ex;

values: vertical-align: -2.505ex; width:84.947ex; height:6.343ex;

values: vertical-align: -0.838ex; width:47.23ex; height:3.343ex;

values: vertical-align: -0.338ex; width:1.222ex; height:2.176ex;

values: vertical-align: -0.838ex; width:24.892ex; height:3.176ex;

values: vertical-align: -0.838ex; width:5.445ex; height:3.176ex;

values: vertical-align: -3.171ex; width:34.064ex; height:7.509ex;

values: vertical-align: -0.838ex; width:19.495ex; height:2.843ex;

values: vertical-align: -1.171ex; width:7.889ex; height:3.509ex;

values: vertical-align: -1.171ex; width:11.206ex; height:3.509ex;

values: vertical-align: -0.671ex; width:2.2ex; height:2.009ex;

values: vertical-align: -1.005ex; width:2.163ex; height:3.176ex;

values: vertical-align: -0.338ex; width:1.138ex; height:1.676ex;

values: vertical-align: -0.338ex; width:2.163ex; height:2.676ex;

values: vertical-align: -1.005ex; width:20.408ex; height:3.343ex;

values: vertical-align: -0.838ex; width:7.647ex; height:3.176ex;

values: vertical-align: -2.505ex; width:54.603ex; height:6.176ex;

values: vertical-align: -1.171ex; margin-left: -0.051ex; width:16.315ex; height:3.509ex;

attrs: columnalign rowspacing columnspacing displaystyle

values: right left right left right left right left right left right left

values: 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em

values: vertical-align: -4.171ex; width:125.399ex; height:9.509ex;

values: vertical-align: -0.838ex; width:2.882ex; height:2.176ex;

values: vertical-align: -0.671ex; width:1.581ex; height:3.176ex;

values: vertical-align: -0.838ex; width:2.718ex; height:2.176ex;

values: vertical-align: -0.671ex; width:2.945ex; height:2.509ex;

values: vertical-align: -0.838ex; width:39.519ex; height:3.343ex;

values: \boldsymbol\mu_n = (\mathbf{X}^{\rm T}\mathbf{X}+\boldsymbol\Lambda_0)^{-1}(\mathbf{X}^{\rm T}\mathbf{X}\hat{\boldsymbol\beta}+\boldsymbol\Lambda_0\boldsymbol\mu_0) .

values: vertical-align: -0.838ex; width:7.277ex; height:2.676ex;

values: vertical-align: -1.005ex; width:123.052ex; height:3.343ex;

values: vertical-align: -3.171ex; width:137.597ex; height:7.509ex;

values: vertical-align: -0.838ex; width:40.739ex; height:3.176ex;

values: \rho(\boldsymbol\beta,\sigma^{2}|\mathbf{y},\mathbf{X}) \propto  \rho(\boldsymbol\beta |\sigma^{2},\mathbf{y},\mathbf{X})   \rho(\sigma^{2}|\mathbf{y},\mathbf{X}),

values: vertical-align: -1.171ex; margin-left: -0.051ex; width:15.821ex; height:3.509ex;

values: \mathcal{N}\left( \boldsymbol\mu_n, \sigma^2\boldsymbol\Lambda_n^{-1} \right)\,

values: vertical-align: -0.838ex; width:20.211ex; height:2.843ex;

values: vertical-align: -0.838ex; width:54.044ex; height:3.343ex;

values: \boldsymbol\Lambda_n=(\mathbf{X}^{\rm T}\mathbf{X}+\mathbf{\Lambda}_0), \quad \boldsymbol\mu_n = (\boldsymbol\Lambda_n)^{-1}(\mathbf{X}^{\rm T}\mathbf{X}\hat{\boldsymbol\beta}+\boldsymbol\Lambda_0\boldsymbol\mu_0) ,

values: vertical-align: -1.838ex; width:61.208ex; height:5.176ex;

values: vertical-align: -0.838ex; width:73.31ex; height:3.343ex;

values: vertical-align: -0.838ex; width:19.988ex; height:3.176ex;

values: vertical-align: -1.838ex; width:13.626ex; height:4.676ex;

values: vertical-align: -1.838ex; width:42.549ex; height:5.176ex;

values: b_{n}=b_{0}+{\frac  {1}{2}}({\mathbf  {y}}^{{{\rm {T}}}}{\mathbf  {y}}+{\boldsymbol  \mu }_{0}^{{{\rm {T}}}}{\boldsymbol  \Lambda }_{0}{\boldsymbol  \mu }_{0}-{\boldsymbol  \mu }_{n}^{{{\rm {T}}}}{\boldsymbol  \Lambda }_{n}{\boldsymbol  \mu }_{n}).

values:
/wiki/Model_evidence
mw-redirect
Model evidence

values: vertical-align: -0.838ex; margin-left: -0.079ex; width:7.219ex; height:2.843ex;

values: vertical-align: -0.338ex; width:2.051ex; height:1.676ex;

values: vertical-align: -0.838ex; margin-left: -0.079ex; width:12.171ex; height:2.843ex;

values: vertical-align: -0.838ex; margin-left: -0.079ex; width:7.018ex; height:2.843ex;

values:
/wiki/Bayesian_model_comparison
mw-redirect
Bayesian model comparison

values: vertical-align: -2.338ex; margin-left: -0.079ex; width:38.449ex; height:5.843ex;

values: p(\mathbf{y}|m)=\int p(\mathbf{y}|\mathbf{X},\boldsymbol\beta,\sigma)\, p(\boldsymbol\beta,\sigma)\, d\boldsymbol\beta\, d\sigma

values: vertical-align: -3.171ex; margin-left: -0.079ex; width:43.664ex; height:7.676ex;

values: vertical-align: -0.338ex; width:1.463ex; height:2.176ex;

values: vertical-align: -2.671ex; margin-left: -0.079ex; width:36.385ex; height:6.509ex;

values:
/wiki/Monte_Carlo_sampling
mw-redirect
Monte Carlo sampling

values:
/wiki/Variational_Bayes
mw-redirect
Variational Bayes

values: vertical-align: -0.838ex; width:16.14ex; height:2.676ex;

values: \boldsymbol\mu_0=0, \mathbf{\Lambda}_0 = c\mathbf{I}

values:
/wiki/Ridge_regression
mw-redirect
Ridge regression

values:
/wiki/Spike_and_slab_variable_selection
mw-redirect
Spike and slab variable selection

values: Wikipedia:WikiProject Fact and Reference Check

values: plainlinks metadata ambox ambox-style ambox-More_footnotes

values: Category:CS1 maint: Uses authors parameter

values:
nofollow
external text
//doi.org/10.1504%2FIJSSS.2015.073223

values: Template:Least squares and regression analysis

values: Template talk:Least squares and regression analysis

values: Pearson product-moment correlation coefficient

values: Kendall tau rank correlation coefficient

values:
/wiki/Partial_least_squares
mw-redirect
Partial least squares

values:
/wiki/Minimum_mean-square_error
mw-redirect
Minimum mean-square error

values: nowraplinks hlist collapsible autocollapse navbox-inner

values:
/wiki/Shape_of_the_distribution
mw-redirect
Shape of the distribution

values: nowraplinks collapsible collapsed navbox-subgroup

values:
/wiki/Population_(statistics)
mw-redirect
Population (statistics)

values:
/wiki/Maximum_likelihood
mw-redirect
Maximum likelihood

values:
/wiki/Median-unbiased_estimator
mw-redirect
Median-unbiased estimator

values:
/wiki/Likelihood_interval
mw-redirect
Likelihood interval

values:
/wiki/Power_(statistics)
mw-redirect
Power (statistics)

values:
/wiki/Permutation_test
mw-redirect
Permutation test

values:
/wiki/Randomization_test
mw-redirect
Randomization test

values:
/wiki/Multiple_comparisons
mw-redirect
Multiple comparisons

values:
/wiki/Rank_statistics
mw-redirect
Rank statistics

values:
/wiki/Sample_median
mw-redirect
Sample median

values: Kruskal–Wallis one-way analysis of variance

values:
CorrelationRegression_analysis
font-size:114%;margin:0 4em
hlist hlist-separated

values: Multivariate adaptive regression splines

values: nowraplinks collapsible uncollapsed navbox-subgroup

values:
/wiki/Multivariate_distribution
mw-redirect
Multivariate distribution

values:
/wiki/Trend_estimation
mw-redirect
Trend estimation

values: List of fields of application of statistics

values: nowraplinks hlist collapsible uncollapsed navbox-inner

values: navigation navbox Statistics padding:3px

values: Category:Articles to be merged from March 2016

values: Category:Articles lacking in-text citations from August 2011

values: Category:All articles lacking in-text citations

values: Discussion about edits from this IP address [ctrl-alt-n]

values: A list of edits made from this IP address [ctrl-alt-y]

values: You are encouraged to create an account and log in; however, it is not mandatory

values: You're encouraged to log in; however, it's not mandatory. [ctrl-alt-o]

values:
/wiki/Bayesian_linear_regression
View the content page [ctrl-alt-c]
c

values: Discussion about the content page [ctrl-alt-t]

values: p-namespaces navigation vectorTabs p-namespaces-label

values: Guidance on how to use and edit Wikipedia

values: About the project, what you can do, where to find things

values: A list of recent changes in the wiki [ctrl-alt-r]

values: portal navigation p-interaction p-interaction-label

values: List of all English Wikipedia pages containing links to this page [ctrl-alt-j]

values: Recent changes in pages linked from this page [ctrl-alt-k]

values:
/wiki/Wikipedia:File_Upload_Wizard
Upload files [ctrl-alt-u]
u

values: A list of all special pages [ctrl-alt-q]

values: Permanent link to this revision of the page

values: Link to connected data repository item [ctrl-alt-g]

values: Printable version of this page [ctrl-alt-p]

values:
uls-settings-trigger
Language settings
0
button
true

values: Баєсова лінійна регресія – Ukrainian

values: mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Bayesian_linear_regression rootpage-Bayesian_linear_regression vector-experimental-print-styles vector-nav-directionality skin-vector action-view


text:
Philtrum
From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
For the publishing house, see Philtrum Press.
Philtrum
Philtrum visible at centre
Dog philtrum
Details
Precursor
medial nasal prominence[1]
Identifiers
TA
A05.1.01.007
FMA
59819
Anatomical terminology
[edit on Wikidata]
The philtrum (Latin: philtrum, Greek: φίλτρον philtron, lit. "love charm"[2]), or medial cleft, is a vertical indentation in the middle area of the upper lip, common to many mammals, extending in humans from the nasal septum to the tubercle of the upper lip. Together with a glandular rhinarium and slit-like nostrils, it is believed[by whom?] to constitute the primitive condition for at least therian mammals. Monotremes lack a philtrum, though this could be due to the specialised, beak-like jaws in living species.[3]
Contents
1 Function
1.1 Development
1.2 Variation
2 Society and culture
3 See also
4 References
Function[edit]
In most mammals, the philtrum is a narrow groove that may carry dissolved odorants from the rhinarium or nose pad to the vomeronasal organ via ducts inside the mouth.[4]
For humans and most primates, the philtrum survives only as a vestigial medial depression between the nose and upper lip.[5]
The human philtrum, bordered by ridges, also is known as the infranasal depression, but has no apparent function. That may be because most higher primates rely more on vision than on smell.[4] Strepsirrhine primates, such as lemurs, still retain the philtrum and the rhinarium, unlike monkeys and apes.[6]
Philtrum
Development[edit]
In humans, the philtrum is formed where the nasomedial and maxillary processes meet during embryonic development. When these processes fail to fuse fully, a cleft lip may result.
Variation[edit]
A flattened or smooth philtrum may be a symptom of fetal alcohol syndrome or Prader–Willi syndrome.[7][8]
A study of boys diagnosed with autism spectrum disorders found that a broader than average philtrum is one of a cluster of physical abnormalities associated with autism.[9]
Society and culture[edit]
In Jewish mythology, each embryo has an angel teaching them all of the wisdom in the world while they are in utero. The Angel lightly taps an infant's upper lip before birth, to silence the infant from telling all the secrets in the universe to the humans who reside in it; the infant then somewhat forgets the Torah they have been taught.[10] Some believers of the myth speculate that this is the cause of the philtrum, but it does not have a basis in traditional Jewish texts.[11]
In Philippine mythology the enchanted creature diwata (or encantado) has smooth skin, with no wrinkles even at the joints, and no philtrum.[12]
In Key Largo (1948), Frank McCloud (Humphrey Bogart) tells a fairy tale to a child, saying that, before birth, the soul knows all the secrets of heaven, but at birth an angel presses a fingertip just above one's lip, which seals us to silence.[13]
In the movie Mr. Nobody, unborn infants are said to have knowledge of all past and future events. As an unborn infant is about to be sent to its mother, the "Angels of Oblivion" lightly tap its upper lip, whereupon the unborn infant forgets everything it knows. The movie follows the life story of one infant, whose lip hadn't been tapped.[14]
In the movie The Prophecy, Archangel Gabriel (Christopher Walken) asks Thomas Dagget, "Do you know how you got that dent in your top lip? Way back, before you were born, I told you a secret, then I put my finger there and I said 'Shhhhh!'"
In Action Comics #719 the Joker says a clue is right under Batman's nose. This leads him to a Dr. Philip Drum.[15]
In the book Prince Ombra by Roderick MacLeish, the "cleft on our upper lips" is attributed to being hushed by a "cavern angel" just before we are born.[16]
See also[edit]
This article uses anatomical terminology; for an overview, see Anatomical terminology.
Cupid's bow
Intermaxillary segment
Toothbrush moustache (philtrum moustache)
Philtrum piercing
References[edit]
Jump up ^ hednk-032—Embryo Images at University of North Carolina
Jump up ^ Liddell, Henry George; Scott, Robert. "φίλτρον, τό, (φιλέω)". A Greek-English Lexicon. republished online at perseus.tufts.edu. Retrieved April 13, 2017.
Jump up ^ Wilfried Westheide, Gunde Rieger, Spezielle Zoologie. Teil 2: Wirbel- oder Schädeltiere, Springer-Verlag, 21/11/2014
^ Jump up to: a b Rossie, James B.; Smith, Timothy D. (12 January 2007). "Ontogeny of the nasolacrimal duct in primates: functional and phylogenetic implications". Journal of Anatomy. doi:10.1111/j.1469-7580.2006.00682.x. PMC 2100270  .
Jump up ^ Hershkovitz, Philip (1977). Living New World monkeys (Platyrrhini): with an introduction to Primates. I. University of Chicago Press. p. 16. ISBN 9780226327884.
Jump up ^ Ankel-Simons, F. (2007). Primate Anatomy (3rd ed.). Academic Press. p. 394. ISBN 978-0-12-372576-9.
Jump up ^ FAS Clinical Archived 2006-05-07 at the Wayback Machine.
Jump up ^ Tran, Nhung T.; Lukefahr, James L. (2013). Koocher, Gerald P.; Norcross, John C.; Greene, Beverly A., eds. "Evaluating the Medical Components of Childhood Development and Behavioral Disorders". Psychologists' Desk Reference (3rd ed.). Oxford University Press: 54.
Jump up ^ Aldridge, Kristina; George, Ian D; Cole, Kimberly K; Austin, Jordan R; Takahashi, T Nicole; Duan, Ye; Miles, Judith H (2011). "Facial phenotypes in subgroups of prepubertal boys with autism spectrum disorders are correlated with clinical phenotypes". Molecular Autism. 2 (1): 15. doi:10.1186/2040-2392-2-15. PMC 3212884  . PMID 21999758.
Jump up ^ Schwartz, Howard, ed. (1994). Gabriel's Palace: Jewish Mystical Tales. OUP USA. p. 57. ISBN 9780195093889.
Jump up ^ Babylonian Talmud; Niddah 30b
Jump up ^ Bane, Theresa (4 September 2013). Encyclopedia of Fairies in World Folklore and Mythology. McFarland. p. 107. ISBN 978-1-4766-1242-3.
Jump up ^ Socher, Abraham (June 22, 2015). "How Humphrey Bogart Came to Cite a Jewish Legend". mosaicmagazine.com. Retrieved April 13, 2017.
Jump up ^ "Mr. Nobody - Angels". YouTube.com. Retrieved April 13, 2017.
Jump up ^ "Hazard's Choice". Action Comics (719). 1996.
Jump up ^ MacLeish, Roderick. Prince Ombra, p. 4 (Macmillan, 2002).
hide
v
t
e
Anatomy of the mouth
Lip
Vermilion border
Frenulum of lower lip
Labial commissure of mouth
Philtrum
Cheek
Buccal fat pad
Roof
Hard palate
Soft palate
Palatine raphe
Incisive papilla
Gums
Interdental papilla
Gingival sulcus
Gingival margin
Gingival fibers
Junctional epithelium
Mucogingival junction
Sulcular epithelium
Stippling
Periodontium
Cementum
Gingiva
Periodontal ligament
Glands
Parotid gland
duct
Submandibular gland
duct
Sublingual gland
duct
Teeth
see tooth anatomy
Tongue
Top
Taste bud
Median sulcus
Terminal sulcus
Foramen cecum
Lingual tonsils
Underside
Frenulum
Fimbriated fold
Sublingual caruncle
Glossoepiglottic folds
Lingual septum
Back of mouth
Oropharynx
fauces
Plica semilunaris of the fauces
Uvula
Palatoglossal arch
Palatopharyngeal arch
Tonsillar fossa
Palatine tonsil
Retrieved from "https://en.wikipedia.org/w/index.php?title=Philtrum&oldid=850366842"
Categories:
Mammal anatomy
Facial features
Lips
Primate anatomy
Horse anatomy
Rodent anatomy
Dog anatomy
Hidden categories:
Pages with unresolved properties
Webarchive template wayback links
Articles containing Latin-language text
Articles containing Greek-language text
Articles with specifically marked weasel-worded phrases from January 2017
Navigation menu
Personal tools
Not logged in
Talk
Contributions
Create account
Log in
Namespaces
Article
Talk
Variants
Views
Read
Edit
View history
More
Search
Navigation
Main page
Contents
Featured content
Current events
Random article
Donate to Wikipedia
Wikipedia store
Interaction
Help
About Wikipedia
Community portal
Recent changes
Contact page
Tools
What links here
Related changes
Upload file
Special pages
Permanent link
Page information
Wikidata item
Cite this page
Print/export
Create a book
Download as PDF
Printable version
Languages
العربية
Asturianu
Bosanski
Čeština
Deutsch
Español
Esperanto
فارسی
Français
한국어
Bahasa Indonesia
Íslenska
Italiano
Nederlands
日本語
Norsk
Polski
Português
Română
Русский
Suomi
Svenska
Tagalog
Türkçe
中文
16 more
Edit links
This page was last edited on 15 July 2018, at 12:53 (UTC).
Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.
Privacy policy
About Wikipedia
Disclaimers
Contact Wikipedia
Developers
Cookie statement
Mobile view
Enable previews

key: html

type: local

value: div

attrs: id class

values: mw-page-base noprint

values: mw-head-base noprint

value: a

attrs: id class lang

values: firstHeading firstHeading en

values: siteSub noprint

attrs: class href

values: mw-jump-link #mw-head

values: mw-jump-link #p-search

attrs: href title

attrs: role class

values:
note
hatnote navigation-not-searchable

value: i

value: th

attrs: colspan style

value: tr

value: img

attrs: alt src width height srcset data-file-width data-file-height

attrs: href class

value: td

values:
/wiki/Latin_language
mw-redirect
Latin language

values:
/wiki/Tubercle_of_the_upper_lip
mw-redirect
Tubercle of the upper lip

values: The material near this tag may use weasel words or too-vague attribution. (January 2017)

values: Wikipedia:Manual of Style/Words to watch

values: checkbox button toctogglecheckbox toctogglecheckbox display:none

attrs: alt src width height class data-file-width data-file-height

values:
/wiki/Cleft_lip_and_palate
mw-redirect
Cleft lip and palate

values:
/wiki/Fetal_alcohol_syndrome
mw-redirect
Fetal alcohol syndrome

values: University of North Carolina at Chapel Hill

attrs: alt src title width height srcset data-file-width data-file-height

values:
nofollow
external text
http://casaa.unm.edu/fas/FAS-cln2.html

values: Psychologists' Desk Reference (page does not exist)

values:
nofollow
external text
//doi.org/10.1186/2040-2392-2-15

values:
/wiki/PubMed_Identifier
mw-redirect
PubMed Identifier

values:
nofollow
external text
//www.ncbi.nlm.nih.gov/pubmed/21999758

values:
/wiki/Babylonian_Talmud
mw-redirect
Babylonian Talmud

values: nowraplinks collapsible autocollapse navbox-inner mw-collapsible mw-made-collapsible

values: Category:Pages with unresolved properties

values: Category:Webarchive template wayback links

values: Category:Articles containing Latin-language text

values: Category:Articles containing Greek-language text

values: Category:Articles with specifically marked weasel-worded phrases from January 2017

values: Discussion about edits from this IP address [ctrl-alt-n]

values: A list of edits made from this IP address [ctrl-alt-y]

values: You are encouraged to create an account and log in; however, it is not mandatory

values: You're encouraged to log in; however, it's not mandatory. [ctrl-alt-o]

values:
/wiki/Philtrum
View the content page [ctrl-alt-c]
c

values:
p-variants
navigation
vectorMenu emptyPortlet
p-variants-label

values:
/w/index.php?title=Philtrum&action=edit
Edit this page [ctrl-alt-e]
e

values: Past revisions of this page [ctrl-alt-h]

values: p-views navigation vectorTabs p-views-label

values:
p-cactions
navigation
vectorMenu emptyPortlet
p-cactions-label

values:
mw-wiki-logo
/wiki/Main_Page
Visit the main page

values:
/wiki/Main_Page
Visit the main page [ctrl-alt-z]
z

values: Featured content – the best of Wikipedia

values: Find background information on current events

values:
/wiki/Special:Random
Load a random article [ctrl-alt-x]
x

values: portal navigation p-navigation p-navigation-label

values:
interlanguage-link interwiki-ast
display: none;

values:
interlanguage-link interwiki-bs
display: none;

values:
https://cs.wikipedia.org/wiki/Philtrum
Philtrum – Czech
cs
cs
interlanguage-link-target

values:
interlanguage-link interwiki-cs
display: none;

values:
https://de.wikipedia.org/wiki/Philtrum
Philtrum – German
de
de
interlanguage-link-target

values:
https://eo.wikipedia.org/wiki/Filtrumo
Filtrumo – Esperanto
eo
eo
interlanguage-link-target

values:
interlanguage-link interwiki-eo
display: none;

values: بوسه‌گاه – Persian

values:
interlanguage-link interwiki-fa
display: none;

values:
https://fr.wikipedia.org/wiki/Philtrum
Philtrum – French
fr
fr
interlanguage-link-target

values:
interlanguage-link interwiki-ko
display: none;

values:
https://id.wikipedia.org/wiki/Filtrum
Filtrum – Indonesian
id
id
interlanguage-link-target

values:
interlanguage-link interwiki-is
display: none;

values:
https://it.wikipedia.org/wiki/Prolabio
Prolabio – Italian
it
it
interlanguage-link-target

values:
interlanguage-link interwiki-it
display: none;

values:
https://nl.wikipedia.org/wiki/Filtrum
Filtrum – Dutch
nl
nl
interlanguage-link-target

values:
interlanguage-link interwiki-nl
display: none;

values:
https://no.wikipedia.org/wiki/Filtrum
Filtrum – Norwegian
no
no
interlanguage-link-target

values:
interlanguage-link interwiki-no
display: none;

values:
interlanguage-link interwiki-pl
display: none;

values:
https://ro.wikipedia.org/wiki/Filtrum
Filtrum – Romanian
ro
ro
interlanguage-link-target

values:
interlanguage-link interwiki-ro
display: none;

values: Губной желобок – Russian

values:
https://fi.wikipedia.org/wiki/Filtrum
Filtrum – Finnish
fi
fi
interlanguage-link-target

values:
interlanguage-link interwiki-fi
display: none;

values:
interlanguage-link interwiki-sv
display: none;

values:
https://tl.wikipedia.org/wiki/Piltrum
Piltrum – Tagalog
tl
tl
interlanguage-link-target

values:
interlanguage-link interwiki-tl
display: none;

values:
https://tr.wikipedia.org/wiki/Philtrum
Philtrum – Turkish
tr
tr
interlanguage-link-target

values:
interlanguage-link interwiki-tr
display: none;

values: All languages (initial selection from common choices by you and others)

values: /static/images/wikimedia-button-1.5x.png 1.5x, /static/images/wikimedia-button-2x.png 2x

values: /static/images/poweredby_mediawiki_132x47.png 1.5x, /static/images/poweredby_mediawiki_176x62.png 2x

values:
suggestions
display: none; font-size: 13px;

values: mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Philtrum rootpage-Philtrum skin-vector action-view


text:
The Wealth of Nations
From Wikipedia, the free encyclopedia
Jump to: navigation, search
This article possibly contains original research. Please improve it by verifying the claims made and adding inline citations. Statements consisting only of original research should be removed. (August 2016) (Learn how and when to remove this template message)
The Wealth of Nations
Author
Adam Smith
Country
Scotland
Language
English
Genre
Economics, Philosophy
Publisher
W. Strahan and T. Cadell, London
Publication date
1776
An Inquiry into the Nature and Causes of the Wealth of Nations, generally referred to by its shortened title The Wealth of Nations, is the magnum opus of the Scottish economist and moral philosopher Adam Smith. First published in 1776, the book offers one of the world's first collected descriptions of what builds nations' wealth, and is today a fundamental work in classical economics. By reflecting upon the economics at the beginning of the Industrial Revolution, the book touches upon such broad topics as the division of labour, productivity, and free markets.
It is the second most cited book in the social sciences published before 1950, behind Karl Marx's Capital.[1]
Contents
[hide]
1 Summary of Wealth of Nations
2 History
2.1 Publishing history
3 Reception and impact
3.1 United States
4 Modern evaluations
5 See also
6 Notes
7 References
8 External links
Summary of Wealth of Nations[edit]
An important theme that persists throughout the work is the idea that the economic system is automatic, and, when left with substantial freedom, able to regulate itself. This is often referred to as the "invisible hand." The ability to self-regulate and to ensure maximum efficiency, however, is limited by externalities, monopolies, tax preferences, lobbying groups, and other "privileges" extended to certain members of the economy at the expense of others.[2]
History[edit]
This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (March 2017) (Learn how and when to remove this template message)
The Wealth of Nations was published 9 March 1776, during the Scottish Enlightenment and the Scottish Agricultural Revolution.[3] It influenced a number of authors and economists, as well as governments and organisations. For example, Alexander Hamilton was influenced in part by The Wealth of Nations to write his Report on Manufactures, in which he argued against many of Smith's policies. Interestingly, Hamilton based much of this report on the ideas of Jean-Baptiste Colbert, and it was, in part, Colbert's ideas that Smith responded to with The Wealth of Nations.
The Wealth of Nations was the product of seventeen years of notes, an observation of conversation among economists of the time concerning economic and societal conditions during the beginning of the Industrial Revolution, and took Smith ten years to produce. The result, An Inquiry to the Wealth of Nations, was a treatise which sought to offer a practical application for reformed economic theory to replace the mercantilist and physiocratic economic theories that were becoming less relevant in the time of industrial progress and innovation. It provided the foundation for new economists, politicians, mathematicians, biologists, and thinkers of all fields to build upon. Irrespective of historical influence, The Wealth of Nations represented a clear shift in the field of economics, comparable to Sir Isaac Newton's Principia Mathematica for physics, Antoine Lavoisier's Traité Élémentaire de Chimie for chemistry, or Charles Darwin's On the Origin of Species for biology.
Publishing history[edit]
Bust of Smith in the Adam Smith Theatre, Kirkcaldy
Five editions of The Wealth of Nations were published during Smith's lifetime: in 1776, 1778,[4] 1784, 1786 and 1789.[5] Numerous editions appeared after Smith's death in 1790. To better understand the evolution of the work under Smith's hand, a team led by Edwin Cannan collated the first five editions. The differences were published along with an edited sixth edition in 1904.[6] They found minor but numerous differences (including the addition of many footnotes) between the first and the second editions, both of which were published in two volumes. The differences between the second and third editions, however, are major: In 1784, Smith annexed these first two editions with the publication of Additions and Corrections to the First and Second Editions of Dr. Adam Smith’s Inquiry into the Nature and Causes of the Wealth of Nations, and he also had published the three-volume third edition of the Wealth of Nations, which incorporated Additions and Corrections and, for the first time, an index. Among other things, the Additions and Corrections included entirely new sections. The fourth edition, published in 1786, had only slight differences from the third edition, and Smith himself says in the Advertisement at the beginning of the book, "I have made no alterations of any kind." Finally, Cannan notes only trivial differences between the fourth and fifth editions—a set of misprints being removed from the fourth and a different set of misprints being introduced.
Reception and impact[edit]
The first edition of the book sold out in six months.[7] The printer William Strahan wrote on 12 April 1776 that David Hume had said that The Wealth of Nations required too much thought to be as popular as Edward Gibbon's The History of the Decline and Fall of the Roman Empire. Strahan also wrote: "What you say of Mr. Gibbon's and Dr. Smith's book is exactly just. The former is the most popular work; but the sale of the latter, though not near so rapid, has been more than I could have expected from a work that requires much thought and reflection (qualities that do not abound among modern readers) to peruse to any purpose".[8] Gibbon wrote to Adam Ferguson on 1 April: "What an excellent work is that with which our common friend Mr. Adam Smith has enriched the public! An extensive science in a single book, and the most profound ideas expressed in the most perspicuous language".[9] The review of the book in the Annual Register was probably written by Whig MP Edmund Burke.[10]
Smith's biographer John Rae contends that The Wealth of Nations shaped government policy soon after it was published. In 1777 the Prime Minister, Lord North, in the first budget after the book was published, got the idea for two new taxes from the book: one on man-servants and the other on property sold at auction. The budget of 1778 introduced the inhabited house duty and the malt tax, both recommended by Smith. In 1779 Smith was consulted by politicians Henry Dundas and Lord Carlisle on the subject of giving Ireland free trade.[11]
The Wealth of Nations was first mentioned in Parliament by the Whig leader Charles James Fox on 11 November 1783: "There was a maxim laid down in an excellent book upon the Wealth of Nations which had been ridiculed for its simplicity, but which was indisputable as to its truth. In that book it was stated that the only way to become rich was to manage matters so as to make one's income exceed one's expenses. This maxim applied equally to an individual and to a nation. The proper line of conduct therefore was by a well-directed economy to retrench every current expense, and to make as large a saving during the peace as possible".[12] However Fox once told Charles Butler sometime after 1785 that he had never read the book and that "There is something in all these subjects which passes my comprehension; something so wide that I could never embrace them myself nor find any one who did".[13] In 1796 when Fox was dining with Lord Lauderdale, Lauderdale remarked that they knew nothing of political economy before Adam Smith wrote. "Pooh," replied Fox, "your Adam Smiths are nothing, but" (he added, turning to the company) "that is his love; we must spare him there". Lauderdale replied: "I think he is everything", to which Fox rejoined: "That is a great proof of your affection".[13] Fox also found Adam Smith "tedious" and believed that one half of The Wealth of Nations could be "omitted with much benefit to the subject".[14]
In an editorial of The Times on 3 August 1787, it was stated: "It is astonishing to consider, how few merchants are acquainted with Smith's Wealth of Nations, or Anderson's History of Commerce, which are certainly books that should be perused by every man who makes trade his pursuit".[15]
The Wealth of Nations was next mentioned in Parliament by Robert Thornton MP in 1787 to support the Commercial Treaty with France. In the same year George Dempster MP referenced it in the debate on the proposal to farm the post-horse duties and in 1788 by a Mr. Hussy on the Wool Exportation Bill.[12] In 1791 the English radical Thomas Paine wrote in his Rights of Man that "Had Mr. Burke possessed talents similar to the author ‘On the Wealth of Nations,’ he would have comprehended all the parts which enter into, and, by assemblage, form a constitution".[16] The Prime Minister, William Pitt, praised Smith in the House of Commons on 17 February 1792: "…an author of our own times now unfortunately no more (I mean the author of a celebrated treatise on the Wealth of Nations), whose extensive knowledge of detail, and depth of philosophical research will, I believe, furnish the best solution to every question connected with the history of commerce, or with the systems of political economy".[17] In the same year it was quoted by Samuel Whitbread MP and Fox (on the division of labour) in the debate on the armament against Russia and also by William Wilberforce in introducing his Bill against the slave trade. It was not mentioned in the House of Lords until 1793, by Lord Lansdowne and Lord Loughborough. Lansdowne said: "With respect to French principles, as they had been denominated, those principles had been exported from us to France, and could not be said to have originated among the population of the latter country. The new principles of government founded on the abolition of the old feudal system were originally propagated among us by the Dean of Gloucester, Mr. Tucker, and had since been more generally inculcated by Dr. Smith in his work on the Wealth of Nations, which had been recommended as a book necessary for the information of youth by Mr. Dugald Stewart in his Elements of the Philosophy of the Human Mind". Loughborough replied that "in the works of Dean Tucker, Adam Smith, and Mr. Stewart, to which allusion had been made, no doctrines inimical to the principles of civil government, the morals or religion of mankind, were contained, and therefore to trace the errors of the French to these causes was manifestly fallacious".[18] On 16 May 1797 Pitt said in the debate on the suspension of cash payments by the Bank of England that Smith was "that great author" but his arguments "though always ingenious" were "sometimes injudicious".[19]
Sir John Mitford, the Solicitor-General, said on 22 December 1798 in speaking on cross-bills (a bill of exchange given in consideration of another bill) that Smith "in his Wealth of Nations, explains the nature and pernicious consequences of this practice with his usual perspicuity and philosophical accuracy".[20] On 5 December 1800 Lord Warwick said in a debate on the price of corn that:
There was hardly any kind of property on which the law did not impose some restraints and regulations with regard to the sale of them, except that of provisions. This was probably done on the principles laid down by a celebrated and able writer, Doctor Adam Smith, who had maintained that every thing ought to be left to its own level. He knew something of that Gentleman, whose heart he knew was as sound as his head; and he was sure that had he lived to this day and beheld the novel state of wretchedness to which the country was now reduced – a state, which as the like had never occurred before, could never have entered into his mind; that Great Man would have reason to blush for some of the doctrines he had laid down. He would now have abundant opportunities of observing that all those artificial means of enhancing the price of provisions, which he had considered as no way mischievous, were practised at this time to a most alarming extent. He would see the Farmer keeping up his produce while the poor were labouring under all the miseries of want, and he would see Forestallers, Regraters, and all kinds of Middle-men making large profits upon it.[21]
Lord Grenville replied that "he must remind him, that so far from there having been any difference in the state of the Country when that great man lived, and the present times, his book was first published at a period, previous to which there had been two or three seasons of great dearth and distress; and during those seasons there were speculators without number, who raised an unfounded and unjust clamour against Forestallers and Regraters, and who proposed that a certain price should be fixed on every article: but all their plans were wisely rejected, and the Treatise on the Wealth of Nations, which came forward soon after, pointed out in the clearest light how absurd and futile they must have been".[21]
In 1800 the Anti-Jacobin Review criticised The Wealth of Nations and Robert Southey in 1812 in the Quarterly Review condemned The Wealth of Nations as a "tedious and hard-hearted book".[22]
In 1803 The Times argued against war with Spain: "She is our best customer; and by the gentle and peaceable stream of commerce, the treasures of the new world flow with greater certainty into English reservoirs, than it could do by the most successful warfare. They come in this way to support our manufactures, to encourage industry, to feed our poor, to pay taxes, to reward ingenuity, to diffuse riches among all classes of people. But for the full understanding of this beneficial circulation of wealth, we must refer to Dr. Adam Smith's incomparable Treatise on the Wealth of Nations".[23] In 1810 a correspondent writing under the pseudonym of Publicola included at the head of his letter Smith's line that "Exclusive Companies are nuisances in every respect" and called him "that learned writer".[24] In 1821 The Times quoted Smith's opinion that the interests of corn dealers and the people were the same.[25]
In 1826 the English radical William Cobbett criticised in his Rural Rides the political economists' hostility to the Poor Law: "Well, amidst all this suffering, there is one good thing; the Scotch political economy is blown to the devil, and the Edinburgh Review and Adam Smith along with it".[26]
The Radical MP Richard Cobden as a young man studied The Wealth of Nations; his copy is still in the library of his home at Dunford House and there are lively marginal notes on the places where Smith condemns British colonial policy. There are none on the passage about the invisible hand.[27] Cobden campaigned for free trade in his agitation against the Corn Laws. On 13 October 1843 Cobden quoted (accurately) Smith's protest against the "plain violation of the most sacred property" of every man derived from his labour.[28] On 8 May 1844 he cited Smith's opposition to slave labour[29] and on 3 July 1844 claimed that Smith had been misrepresentated by protectionists as a monopolist.[30] On 8 October 1849 Cobden claimed that he had "gone through the length and breadth of this country, with Adam Smith in my hand, to advocate the principles of Free Trade." He also said he had tried "to popularise to the people of this country, and of the Continent, those arguments with which Adam Smith, David Hume, Ricardo, and every man who has written on this subject, have demonstrated the funding system to be injurious to mankind, and unjust in principle".[31] Cobden believed it to be morally wrong to lend money to be spent on war. When The Times claimed the political economists were against Cobden on this, Cobden wrote on 16 October 1849: "I can quote Adam Smith whose authority is without appeal now in intellectual circles, it gives one the basis of science upon which to raise appeals to the moral feelings".[32] When in 1850 the Russian government attempted to raise a loan, ostensibly for the construction of a railway from St. Petersburg to Moscow, but actually to cover the deficit brought about by its war against Hungary, Cobden said on 18 January: "I take my stand on one of the strongest grounds in stating that Adam Smith and other great authorities on political economy are opposed to the very principle of such loans".[33] In 1863, during Cobden's dispute with The Times over its claims that his fellow Radical John Bright wanted to divide the land of the rich amongst the poor, Cobden read to a friend the passage in the Wealth of Nations which criticised primogeniture and entail. Cobden said that if Bright had been as plain-speaking as Smith, "how he would have been branded as an incendiary and Socialist".[34] On 23 November 1864 Cobden proclaimed: "If I were five-and-twenty or thirty, instead of, unhappily, twice that number of years, I would take Adam Smith in hand—I would not go beyond him, I would have no politics in it – I would take Adam Smith in hand, and I would have a League for free trade in Land just as we had a League for free trade in Corn. You will find just the same authority in Adam Smith for the one as for the other; and if it were only taken up as it must be taken up to succeed, not as a political, revolutionary, Radical, Chartist notion, but taken up on politico-economic grounds, the agitation would be certain to succeed".[35]
The Liberal statesman William Ewart Gladstone chaired the meeting of the Political Economy Club to celebrate the centenary of the publication of The Wealth of Nations.[36]
The Liberal historian Lord Acton believed that The Wealth of Nations gave a "scientific backbone to liberal sentiment"[37] and that it was the "classic English philosophy of history".[38]
United States[edit]
James Madison, in a speech given in Congress on 2 February 1791, cited The Wealth of Nations in opposing a national bank: "The principal disadvantages consisted in, 1st. banishing the precious metals, by substituting another medium to perform their office: This effect was inevitable. It was admitted by the most enlightened patrons of banks, particularly by Smith on the Wealth of Nations".[39] Thomas Jefferson, writing to John Norvell on 14 June 1807, claimed that on "the subjects of money & commerce, Smith's Wealth of Nations is the best book to be read, unless Say's Political Economy can be had, which treats the same subject on the same principles, but in a shorter compass & more lucid manner".[40]
Modern evaluations[edit]
Bustling with work and activity, "The Wealth of the Nation" by Seymour Fogel is an interpretation of the theme of Social Security.
George Stigler attributes to Smith "the most important substantive proposition in all of economics" and foundation of resource-allocation theory. It is that, under competition, owners of resources (labour, land, and capital) will use them most profitably, resulting in an equal rate of return in equilibrium for all uses (adjusted for apparent differences arising from such factors as training, trust, hardship, and unemployment).[41] He also describes Smith's theorem that "the division of labour is limited by the extent of the market" as the "core of a theory of the functions of firm and industry" and a "fundamental principle of economic organisation."[42]
Paul Samuelson finds in Smith's pluralist use of supply and demand—as applied to wages, rents, and profit—a valid and valuable anticipation of the general equilibrium modelling of Walras a century later. Moreover, Smith's allowance for wage increases in the short and intermediate term from capital accumulation and invention added a realism missed later by Malthus, Ricardo, and Marx in their propounding a rigid subsistence-wage theory of labour supply.[43]
In noting the last words of the Wealth of Nations,
If any of the provinces of the British empire cannot be made to contribute towards the support of the whole empire, it is surely time that Great Britain should free herself from the expence of defending those provinces in time of war, and of supporting any part of their civil or military establishments in time of peace, and endeavour to accommodate her future views and designs to the real mediocrity of her circumstances.[44]
Ronald Coase suggests that if Smith's earlier proposal of granting colonies representation in the British parliament proportional to their contributions to public revenues had been followed, "there would have been no 1776, … America would now be ruling England, and we [in America] would be today celebrating Adam Smith not simply as the author of the Wealth of Nations, but hailing him as a founding father."[45]
Mark Blaug argues that it was Smith's achievement to shift the burden of proof against those maintaining that the pursuit of self-interest does not achieve social good. But he notes Smith's relevant attention to definite institutional arrangements and process as disciplining self-interest to widen the scope of the market, accumulate capital, and grow income.[46]
Economic anthropologist David Graeber argues that throughout antiquity, one can identify many different systems of credit and later monetary exchange, drawing evidence for his argument from historical and also ethnographical records, that the traditional explanation for the origins of monetary economies from primitive bartering systems, as laid out by Adam Smith, doesn't find empirical support.[47] The author argues that credit systems developed as means of account long before the advent of coinage around 600 BCE, and can still be seen operating in non-monetary economies. The idea of barter, on the other hand, seems only to apply to limited exchanges between societies that had infrequent contact and often in a context of ritualised warfare, rendering its conceptualisation among economists as a myth.[48] As an alternative explanation for the creation of economic life, the author suggests that it originally related to social currencies, closely related to non-market quotidian interactions among a community and based on the "everyday communism" that is based on mutual expectations and responsibilities among individuals. This type of economy is, then, contrasted with the moral foundations of exchange based on formal equality and reciprocity (but not necessarily leading to market relations) and hierarchy, based on clear inequalities that tend to crystallise in customs and castes.[48]
See also[edit]
The Theory of Moral Sentiments (1759), Adam Smith's other major work
The National Gain, a pamphlet by Finnish–Swedish economist and politician Anders Chydenius which preceded The Wealth of Nations and which had similar ideas.
Notes[edit]
Jump up ^ Green, Elliott (12 May 2016). "What are the most-cited publications in the social sciences (according to Google Scholar)?". LSE Impact Blog. London School of Economics.
Jump up ^ GradeSaver. "The Wealth of Nations Summary". www.gradesaver.com. Retrieved 2016-10-02.
Jump up ^ See Smith, Adam (1776). An Inquiry into the Nature and Causes of the Wealth of Nations. 1 (1 ed.). London: W. Strahan. Retrieved 2012-12-07. , volume 2 via Google Books
Jump up ^ See Smith, Adam (1778). An Inquiry into the Nature and Causes of the Wealth of Nations. 1 (2 ed.). London: W. Strahan; T.Cadell. Retrieved 10 March 2015. ; Smith, Adam (1778). An Inquiry into the Nature and Causes of the Wealth of Nations. 2 (2 ed.). London: W. Strahan; T.Cadell. Retrieved 10 March 2015. via Google Books
Jump up ^ See Smith, Adam (1789). An Inquiry into the Nature and Causes of the Wealth of Nations. 1 (5 ed.). London: A. Strahan; T.Cadell. Retrieved 9 March 2015. ; Smith, Adam (1789). An Inquiry into the Nature and Causes of the Wealth of Nations. 2 (5 ed.). London: A. Strahan; T.Cadell. Retrieved 9 March 2015. ; Smith, Adam (1789). An Inquiry into the Nature and Causes of the Wealth of Nations. 3 (5 ed.). London: A. Strahan; T.Cadell. Retrieved 9 March 2015. via Google Books
Jump up ^ An Inquiry into the Nature and Causes of the Wealth of Nations, by Adam Smith. London: Methuen and Co., Ltd., ed. Edwin Cannan, 1904. Fifth edition.
Jump up ^ John Rae, Life of Adam Smith (London: Macmillan & Co., 1895), p. 285.
Jump up ^ Rae, pp. 285–86.
Jump up ^ Rae, p. 287.
Jump up ^ Rae, p. 286.
Jump up ^ Rae, p. 294.
^ Jump up to: a b Rae, p. 290.
^ Jump up to: a b Rae, p. 289.
Jump up ^ L. G. Mitchell, Charles James Fox (Penguin, 1997), p. 185.
Jump up ^ The Times (3 August 1787), p. 2.
Jump up ^ Thomas Paine, Rights of Man, Common Sense, and Other Political Writings (Oxford University Press, 1995), p. 126.
Jump up ^ John Ehrman, The Younger Pitt. The Years of Acclaim (London: Constable, 1969), p. 267, n. 1.
Jump up ^ Rae, p. 291.
Jump up ^ John Ehrman, The Younger Pitt. The Consuming Struggle (London: Constable, 1996), p. 12.
Jump up ^ The Times (24 December 1798), p. 4.
^ Jump up to: a b The Times (6 December 1800), p. 2.
Jump up ^ J. J. Sack, From Jacobite to Conservative. Reaction and orthodoxy in Britain, c. 1760–1832 (Cambridge University Press, 2004), p. 182.
Jump up ^ The Times (25 October 1803), p. 2.
Jump up ^ The Times (8 February 1810), p. 2.
Jump up ^ The Times (17 September 1821), p. 2.
Jump up ^ William Cobbett, Rural Rides (Penguin, 2001), p. 335.
Jump up ^ William D. Grampp, The Manchester School of Economics (London: Oxford University Press, 1960), p. 103.
Jump up ^ John Bright and J. E. Thorold Rogers (eds.), Speeches on Questions of Public Policy by Richard Cobden, M.P. Volume I (London: T. Fisher Unwin, 1908), p. 45.
Jump up ^ Bright and Thorold Rogers, Volume I, p. 92.
Jump up ^ Bright and Thorold Rogers, Volume I, pp. 104–05.
Jump up ^ John Bright and J. E. Thorold Rogers (eds.), Speeches on Questions of Public Policy by Richard Cobden, M.P. Volume II (London: T. Fisher Unwin, 1908), pp. 399–400.
Jump up ^ Wendy Hinde, Richard Cobden. A Victorian Outsider (Yale University Press, 1987), p. 204.
Jump up ^ Bright and Thorold Rogers, Volume II, p. 406.
Jump up ^ Donald Read, Cobden and Bright. A Victorian Political Partnership (Edward Arnold, 1967), p. 189.
Jump up ^ Bright and Thorold Rogers, Volume II, p. 493.
Jump up ^ H. C. G. Matthew, Gladstone. 1875–1898 (Oxford University Press, 1995), p. 20.
Jump up ^ G. E. Fasnacht, Acton's Political Philosophy. An Analysis (London: Hollis and Carter, 1952), p. 145.
Jump up ^ Fasnacht, p. 241.
Jump up ^ James Madison, Writings (The Library of America, 1999), p. 481.
Jump up ^ Thomas Jefferson, Writings (The Library of America, 1984), p. 1176.
Jump up ^ George J. Stigler (1976). "The Successes and Failures of Professor Smith," Journal of Political Economy, 84(6), p. 1202 (pp. 1199–1213). Also published as Selected Papers, No. 50 (PDF), Graduate School of Business, University of Chicago.
Jump up ^ George J. Stigler, 1951. "The Division of Labor Is Limited by the Extent of the Market." Journal of Political Economy, 59(3), pp. 185, 193. Reprinted in J.M. Buchanan and Y.J. Yoon, ed., 1994, The Return to Increasing Returns, pp. 47, 58.
Jump up ^ Paul A. Samuelson (1977). "A Modern Theorist's Vindication of Adam Smith," American Economic Review, 67(1), p. 42. Reprinted in J.C. Wood, ed., Adam Smith: Critical Assessments, pp. 498–509. Preview.
Jump up ^ Smith (1776). Bk. V: Of the Revenue of the Sovereign or Commonwealth, ch. 3 Of Public Debts, para. 92.
Jump up ^ R. H. Coase (1977). "The Wealth of Nations," Economic Inquiry 15(3), pp. 323–25 (309–25). Press + button or Ctrl+.
Jump up ^ Mark Blaug (1997). Economic Theory in Retrospect, 5th ed., in ch. 2, sect. 19, "Adam Smith as an Economist, pp. 59–62.
Jump up ^ Graeber, David (2010). Debt: the first 5,000 years. Brooklyn, NY: Melville House. ISBN 9781933633862.
^ Jump up to: a b Johnson, David V. (February 15, 2012). "What We Owe to Each Other An Interview with David Graeber, Part 1". Boston Review. Retrieved February 20, 2012.
References[edit]
Smith, Adam. The Wealth of Nations: A Translation into Modern English, Industrial Systems Research, 2015. ISBN 978-0-906321-70-6 [1]
An Inquiry into the Nature and Causes of the Wealth of Nations: A Selected Edition Adam Smith (Author), Kathryn Sutherland (Editor), 2008, Oxford Paperbacks, Oxford, UK; ISBN 978-0-19-953592-7
Adam Smith's The Wealth of Nations: A modern-day interpretation of an economic classic. Karen McCreadie, 2009, Infinite Ideas, Oxford, UK; ISBN 978-1-906821-03-6
O'Rourke, P. J. (2006), On The Wealth of Nations, Books That Changed the World, Atlantic Monthly Press, ISBN 978-0871139498
External links[edit]
Media related to The Wealth of Nations at Wikimedia Commons
Wikisource has original text related to this article:
The Wealth of Nations
The Wealth of Nations at MetaLibri Digital Library
The Theory of Moral Sentiments at MetaLibri Digital Library
[show]
v
t
e
Adam Smith
Books
Essays on Philosophical Subjects
Lectures on Jurisprudence
The Theory of Moral Sentiments
The Wealth of Nations
Theories
Classical economics
Invisible hand
[show]
v
t
e
Property
By owner
Communal land
Marital property (USA)
Cooperative
Estate in land
Private
Public
State
Crown land
By nature
Croft
Intangible
Intellectual
indigenous
Personal
Tangible
immovable
real
Common resources
Common land
Common-pool resource
Digital
Global
Information
Knowledge
Theory
Bundle of rights
Commodity
fictitious commodities
Common good (economics)
Excludability
First possession
appropriation
homestead principle
Free rider problem
Game theory
Georgism
Gift economy
Labor theory of property
Law of rent
rent-seeking
Legal plunder
Natural rights
Ownership
common
customary
self
state
Property rights
primogeniture
usufruct
women's
Right to property
Rivalry
Tragedy of the commons
anticommons
Applications
Acequia (watercourse)
Ejido (agrarian land)
Forest types
Inheritance
Land tenure
Property law
alienation
easement
restraint on alienation
real estate
title
Rights
Air
Fishing
Forest-dwelling (India)
Freedom to roam
Grazing
pannage
Hunting
Land
aboriginal
indigenous
squatting
Littoral
Mineral
Bergregal
Right of way
Water
prior-appropriation
riparian
Disposession/
redistribution
Bioprospecting
Collectivization
Eminent domain
Enclosure
Eviction
Expropriation
Farhud
Forced migration
population transfer
Illegal fishing
Illegal logging
Land reform
Legal plunder
Piracy
Poaching
Primitive accumulation
Privatization
Regulatory taking
Slavery
bride-buying
human trafficking
wage
wife selling
Tax
inheritance
poll
progressive
property
Theft
Scholars
(key work)
Frédéric Bastiat
Ronald Coase
Henry George
Garrett Hardin
David Harvey
John Locke
Two Treatises of Government
Karl Marx
Marcel Mauss
The Gift
John Stuart Mill
Elinor Ostrom
Karl Polanyi
The Great Transformation
Pierre-Joseph Proudhon
What Is Property?
David Ricardo
Murray N. Rothbard
The Ethics of Liberty
Jean-Jacques Rousseau
The Social Contract
Adam Smith
The Wealth of Nations
Categories: Property
Property law
by country
Authority control
BNF: cb12099112r (data)
Retrieved from "https://en.wikipedia.org/w/index.php?title=The_Wealth_of_Nations&oldid=823613490"
Categories:
1776 books
1776 in economics
1776 in Scotland
Books about capitalism
Books about wealth distribution
Books by Adam Smith
Classical liberalism
Classical economics books
History books about civilization
Political philosophy literature
Hidden categories:
Articles that may contain original research from August 2016
All articles that may contain original research
Use British English from March 2012
Use dmy dates from March 2012
Articles needing additional references from March 2017
All articles needing additional references
Wikipedia articles with BNF identifiers
Navigation menu
Personal tools
Not logged in
Talk
Contributions
Create account
Log in
Namespaces
Article
Talk
Variants
Views
Read
Edit
View history
More
Search
Navigation
Main page
Contents
Featured content
Current events
Random article
Donate to Wikipedia
Wikipedia store
Interaction
Help
About Wikipedia
Community portal
Recent changes
Contact page
Tools
What links here
Related changes
Upload file
Special pages
Permanent link
Page information
Wikidata item
Cite this page
Print/export
Create a book
Download as PDF
Printable version
In other projects
Wikimedia Commons
Wikisource
Languages
العربية
Български
Català
Čeština
Deutsch
Ελληνικά
Español
Esperanto
Euskara
فارسی
Français
Galego
ગુજરાતી
한국어
Հայերեն
हिन्दी
Ido
Bahasa Indonesia
Italiano
עברית
ქართული
Македонски
Bahasa Melayu
Nederlands
日本語
Norsk
ਪੰਜਾਬੀ
Polski
Português
Română
Русский
Shqip
Simple English
Suomi
Svenska
Tagalog
ไทย
Türkçe
Українська
Tiếng Việt
文言
吴语
粵語
中文
35 more
Edit links
This page was last edited on 2 February 2018, at 09:24.
Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.
Privacy policy
About Wikipedia
Disclaimers
Contact Wikipedia
Developers
Cookie statement
Mobile view
Enable previews

values: mw-page-base noprint

values: mw-head-base noprint

values: firstHeading firstHeading en

values: siteSub noprint

values: jump-to-nav mw-jump

value: b

value: span

value: small

values: plainlinks metadata ambox ambox-content ambox-Original_research

values: Edit section: Summary of Wealth of Nations

values: Help:Introduction to referencing with Wiki Markup/1

values: plainlinks metadata ambox ambox-content ambox-Refimprove

values: Philosophiae Naturalis Principia Mathematica

attrs: alt src width height class srcset data-file-width data-file-height

values:
/wiki/Annual_Register
mw-redirect
Annual Register

values:
/wiki/George_Dempster_(lawyer)
mw-redirect
George Dempster (lawyer)

values: Alexander Wedderburn, 1st Earl of Rosslyn

values: John Freeman-Mitford, 1st Baron Redesdale

values:
/wiki/Allocation_of_resources
mw-redirect
Allocation of resources

values:
/wiki/Industrial_organisation
mw-redirect
Industrial organisation

values:
/wiki/General_equilibrium
mw-redirect
General equilibrium

values:
nofollow
external text
https://www.jstor.org/pss/1831274

values:
nofollow
external text
https://www.jstor.org/pss/1826433

values:
nofollow
external text
https://www.jstor.org/pss/1815879

values: -moz-column-width: 30em; -webkit-column-width: 30em; column-width: 30em; list-style-type: decimal;

values:
nofollow
http://metalibri.wikidot.com/
external text

values: nowraplinks collapsible autocollapse navbox-inner

values:
/wiki/State_property
mw-redirect
State property

values:
/wiki/Common_resources
mw-redirect
Common resources

values:
/wiki/Appropriation_(economics)
mw-redirect
Appropriation (economics)

values:
/wiki/Free_rider_problem
mw-redirect
Free rider problem

values: List of types of formally designated forests

values: The Scheduled Tribes and Other Traditional Forest Dwellers (Recognition of Forest Rights) Act, 2006

values:
/wiki/Forced_migration
mw-redirect
Forced migration

values:
/wiki/Illegal_fishing
mw-redirect
Illegal fishing

values:
/wiki/Tax_per_head
mw-redirect
Tax per head

values:
/wiki/Murray_N._Rothbard
mw-redirect
Murray N. Rothbard

values: nowraplinks hlist collapsible autocollapse navbox-inner

values: Category:Books about wealth distribution

values: Category:History books about civilization

values: Category:Articles that may contain original research from August 2016

values: Category:All articles that may contain original research

values: Category:Use British English from March 2012

values: Category:Articles needing additional references from March 2017

values: Category:All articles needing additional references

values: Category:Wikipedia articles with BNF identifiers

values: Discussion about edits from this IP address [ctrl-alt-n]

values: A list of edits made from this IP address [ctrl-alt-y]

values: You are encouraged to create an account and log in; however, it is not mandatory

values: You're encouraged to log in; however, it's not mandatory. [ctrl-alt-o]

values:
/wiki/The_Wealth_of_Nations
View the content page [ctrl-alt-c]
c

values: Discussion about the content page [ctrl-alt-t]

values: p-namespaces navigation vectorTabs p-namespaces-label

values:
p-variants
navigation
vectorMenu emptyPortlet
p-variants-label

values: Past revisions of this page [ctrl-alt-h]

values: p-views navigation vectorTabs p-views-label

values:
p-cactions
navigation
vectorMenu emptyPortlet
p-cactions-label

values:
mw-wiki-logo
/wiki/Main_Page
Visit the main page

values:
/wiki/Main_Page
Visit the main page [ctrl-alt-z]
z

values: Featured content – the best of Wikipedia

values: Find background information on current events

values:
/wiki/Special:Random
Load a random article [ctrl-alt-x]
x

values: portal navigation p-navigation p-navigation-label

values: Guidance on how to use and edit Wikipedia

values: About the project, what you can do, where to find things

values: A list of recent changes in the wiki [ctrl-alt-r]

values: portal navigation p-interaction p-interaction-label

values: List of all English Wikipedia pages containing links to this page [ctrl-alt-j]

values: Recent changes in pages linked from this page [ctrl-alt-k]

values:
/wiki/Wikipedia:File_Upload_Wizard
Upload files [ctrl-alt-u]
u

values: A list of all special pages [ctrl-alt-q]

values: Permanent link to this revision of the page

values: Link to connected data repository item [ctrl-alt-g]

values: Printable version of this page [ctrl-alt-p]

values: portal navigation p-wikibase-otherprojects p-wikibase-otherprojects-label

values: ثروة الأمم – Arabic

values: Богатството на народите – Bulgarian

values:
interlanguage-link interwiki-bg
display: none;

values: Indagació sobre la naturalesa i les causes de la riquesa de les nacions – Catalan

values: interlanguage-link interwiki-ca badge-Q17437796 badge-featuredarticle

values: Pojednání o podstatě a původu bohatství národů – Czech

values:
interlanguage-link interwiki-cs
display: none;

values:
interlanguage-link interwiki-de
display: none;

values: Ο Πλούτος των Εθνών – Greek

values:
interlanguage-link interwiki-el
display: none;

values: interlanguage-link interwiki-es badge-Q17437796 badge-featuredarticle

values:
interlanguage-link interwiki-eo
display: none;

values:
interlanguage-link interwiki-eu
display: none;

values: ثروت ملل – Persian

values:
interlanguage-link interwiki-fa
display: none;

values: Recherches sur la nature et les causes de la richesse des nations – French

values: interlanguage-link interwiki-fr badge-Q17437796 badge-featuredarticle

values:
interlanguage-link interwiki-gl
display: none;

values: ધ વેલ્થ ઑફ નેશનઝ – Gujarati

values:
interlanguage-link interwiki-gu
display: none;

values:
interlanguage-link interwiki-ko
display: none;

values: Ազգերի հարստություն – Armenian

values:
interlanguage-link interwiki-hy
display: none;

values: द वेल्थ ऑफ नेशन्स – Hindi

values:
interlanguage-link interwiki-io
display: none;

values: An Inquiry Into the Nature and Causes of the Wealth of Nations – Indonesian

values:
interlanguage-link interwiki-it
display: none;

values: עושר העמים – Hebrew

values:
interlanguage-link interwiki-he
display: none;

values: გამოკვლევა ხალხთა სიმდიდრის ბუნებისა და მიზეზების შესახებ – Georgian

values:
interlanguage-link interwiki-ka
display: none;

values: Богатството на народите – Macedonian

values:
interlanguage-link interwiki-mk
display: none;

values:
interlanguage-link interwiki-nl
display: none;

values: 諸国民の富の性質と原因の研究 – Japanese

values:
interlanguage-link interwiki-ja
display: none;

values: ਦ ਵੈਲਥ ਆਫ਼ ਨੇਸ਼ਨਜ – Punjabi

values:
interlanguage-link interwiki-pa
display: none;

values: Badania nad naturą i przyczynami bogactwa narodów – Polish

values:
interlanguage-link interwiki-pt
display: none;

values: Исследование о природе и причинах богатства народов – Russian

values:
interlanguage-link interwiki-sq
display: none;

values:
interlanguage-link interwiki-simple
display: none;

values: ความมั่งคั่งของประชาชาติ – Thai

values:
interlanguage-link interwiki-th
display: none;

values: Дослідження про природу і причини багатства народів – Ukrainian

values:
interlanguage-link interwiki-uk
display: none;

values: Tìm hiểu về bản chất và nguồn gốc của cải của các quốc gia – Vietnamese

values:
interlanguage-link interwiki-vi
display: none;

values:
interlanguage-link interwiki-wuu
display: none;

values:
interlanguage-link interwiki-zh-yue
display: none;

values: mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-The_Wealth_of_Nations rootpage-The_Wealth_of_Nations skin-vector action-view