Introduction to Bayesian EconometricsThis textbook explains the basic ideas of subjective probability and shows how subjective probabilities must obey the usual rules of probability to ensure coherency. It defines the likelihood function, prior distributions and posterior distributions. It explains how posterior distributions are the basis for inference and explores their basic properties. Various methods of specifying prior distributions are considered, with special emphasis on subject-matter considerations and exchange ability. The regression model is examined to show how analytical methods may fail in the derivation of marginal posterior distributions. The remainder of the book is concerned with applications of the theory to important models that are used in economics, political science, biostatistics and other applied fields. New to the second edition is a chapter on semiparametric regression and new sections on the ordinal probit, item response, factor analysis, ARCH-GARCH and stochastic volatility models. The new edition also emphasizes the R programming language. |
Contents
Introduction | 3 |
Posterior Distributions and Inference | 21 |
Prior Distributions | 43 |
Classical Simulation | 65 |
Basics of Markov Chains | 79 |
Simulation by MCMC Methods | 93 |
Linear Regression and Extensions | 115 |
Semiparametric Regression | 148 |
Multivariate Responses | 169 |
Time Series | 187 |
Endogenous Covariates and Sample Selection | 206 |
Probability Distributions and Matrix Theorems | 223 |
B Computer Programs for MCMC Calculations | 234 |
| 245 | |
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Common terms and phrases
95 percent credibility analyzed approximate assume assumption autocorrelation axioms Bayes factor Bayesian approach Bayesian inference beta distribution binary probit chapter Chib choose compute conditional distribution conditional posterior distribution conjugate prior consider convergence correlation covariates credibility interval define denoted density function derivatives Dirichlet distribution draw econometrics Equation estimate example find finite firm first fixed frequentist gamma distribution Gibbs algorithm hyperparameters identified implies independent integral invariant distribution joint distribution kernel knots large number latent data likelihood function linear regression linear regression model logit model marginal distribution marginal likelihood marginal posterior distribution matrix MCMC algorithm MCMC methods MH algorithm normal distribution outcomes panel data parameters percent credibility interval posterior distribution predictive distribution prior distribution probability distribution probit model proposal density random variable reflect regression coefficients response variable sample simulation specification specify standard statistics Summary of Posterior target distribution term theorem Tobit truncated values vector verify zero