Michel Lubrano

Bayesian Inference on GARCH Models Using the Gibbs Sampler

This paper explains how the Gibbs sampler can be used to perform Bayesian inference on GARCH models. Although the Gibbs sampler is usually based on the analytical knowledge of the full conditional posterior densities, such knowledge is not available in regression models with GARCH errors. We show that the Gibbs sampler can be combined with a unidimensional deterministic integration rule applied to each coordinate of the posterior density.

Bayesian analysis of switching regression models

Abstract The paper considers a class of switching regression models where the change of regime is represented by a min operator. After reviewing a maximum likehood method, a local identification criterion is proposed. Contrary to classical analysis, it is shown that Bayesian analysis requires here local identification everywhere on the parameter space. The paper then proposes a Monte Carlo procedure to compute posterior moments with an importance function based on an approximate posterior density of the model. Feasibility of the method is shown in a numerical example and then in an economic example.

Decision Theory and Bayesian Inference

PURPOSE To equip the students with skills to build statistical models for non-trivial problems when data is sparse and expert opinion needs to be incorporated and to use the key features of a Bayesian problem and algorithms for Bayesian Analysis. OBJECTIVES By the end of this course the student should be able to; (i) Explain and apply Bayes’ rule and other decision rules. (ii) Explain the likelihood principle and derive a posterior distribution from a prior distribution. (iii) Perform classification, hypothesis testing and estimation. (iv) Explain the subjectivism point of view. (v) Apply Bayesian inference and analysis for the normal and binomial distributions. (vi) Apply the basic concepts in decision analysis.