Bayesian Econometric Methods
Cambridge University Press, Jan 15, 2007 - Business & Economics - 380 pages
This volume in the Econometric Exercises series contains questions and answers to provide students with useful practice, as they attempt to master Bayesian econometrics. In addition to many theoretical exercises, this book contains exercises designed to develop the computational tools used in modern Bayesian econometrics. The latter half of the book contains exercises that show how these theoretical and computational skills are combined in practice, to carry out Bayesian inference in a wide variety of models commonly used by econometricians. Aimed primarily at advanced undergraduate and graduate students studying econometrics, this book may also be useful for students studying finance, marketing, agricultural economics, business economics or, more generally, any field which uses statistics. The book also comes equipped with a supporting website containing all the relevant data sets and MATLAB computer programs for solving the computational exercises.
The linear regression model
The linear regression model with general covariance matrix
associated Bayes factor Bayesian point estimate burn-in calculate Chapter coefﬁcients complete conditional complete posterior conditionals component computational conditional posterior conjugate prior Consider covariance matrix data set deﬁned Deﬁnition denote derive draws Econometrics equation error Exercise explanatory variables exponential ﬁnite ﬁrst ﬁt follows frequentist gamma Geweke Gibbs sampler given HPD interval hyperparameters implies importance sampling iterations Jeffreys joint posterior kernel Laplace approximation latent data likelihood function linear regression linear regression model loss function marginal likelihood marginal posterior means and standard mixture Monte Carlo integration normal linear regression normal-gamma observations obtain parameterization parameters point estimate Poirier posterior density posterior distribution posterior mean posterior probability posterior simulator predictive density prior density probit model quadratic loss random variable reparameterization Solution Speciﬁcally standard deviations Statistical Suppose Table theorem values vector yields zero
Page 1 - Theorem provides the key to the ways in which beliefs should fit together in the light of changing evidence. The goal, in effect, is to establish rules and procedures for individuals concerned with disciplined uncertainty accounting. The theory is not descriptive, in the sense of claiming to model actual behavior. Rather, it is prescriptive, in the sense of saying "if you wish to avoid the possibility of these undesirable consequences you must act in the following way.
Page 1 - ... inconsistencies. The theory establishes that expected utility maximization provides the basis for rational decision making and that Bayes' Theorem provides the key to the ways in which beliefs should fit together in the light of changing evidence. The goal, in effect, is to establish rules...