Predictive Updating Methods with Application to Bayesian Classification
Rong Chen, Jun S. Liu · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1996
SUMMARY We propose algorithms based on random draws from predictive distributions of unknown quantities (missing values, for instance). This procedure can either be iterative, which is a special variation of the Gibbs sampler, or be sequential, which is a variation of sequential imputation. In the latter case one can update the posterior distribution with new observations easily. The methods proposed have intuitive statistical implications and can be generalized to accommodate other Bayesian-like procedures. We display some applications of the method in connection with the Bayesian bootstrap, classification, hierarchical models and selection of variables. In particular, as an application of the method, we present a unified treatment of switching regression models driven by a general binary process, and we develop a Bayesian testing procedure. Some simulations and a real example are used to illustrate the methods proposed.