Monte Carlo Bayesian Methods for Discrete Regression Models and Categorical Time Series

Abstract

Abstract Discrete regression models and categorical time series are viewed as a constrained Bayesian hierarchical model. A Monte Carlo approach employing latent data variables is adopted, which leads to a conceptually simple and computationally feasible approach to this class of problems. We offer two illustrative examples. The first analyzes a binomial regression model and computes influence diagnostics based on Kullback-Leibler divergences between full and reduced dataset posteriors for a parameter of interest. The second example involves state space model analysis of a binary time series produced by monitoring an infant’s sleep patterns.