The focus of this research is on solutions of the Bayesian multiple integration problem in econometrics, using a class of numerical integration procedures widely known as Gibbs samplers. The objectives of the project are to make Bayesian inference as routine and reliable as classical methods in econometrics, and to provide solutions of outstanding econometric problems on which little progress has been made heretofore using either Bayesian or classical approaches. The project involves extensions of the analysis of Gibbs samplers to develop central limit theorems appropriate to the systematic assessment of numerical accuracy, evaluate senstivity to initial conditions, and apply these methods ot underidentified models. The project will also exploit the successive conditioning fundamental to Gibbs sampling and the related technique of data augmentation, to develop a modular treatment of most econometric models. These modules include semi-informative priors in regressions, censored regression, heteroskedasticity, seemingly unrelated regressions, the multinominal probit model, reduced rank regression, the latent factor model, multivariatre (moving average) autoregression, and state space models.
