Comparison of Generalized Additive Regression Models

• Activity Number: 320
• Type: Topic Contributed
• Date/Time: Wednesday, August 6, 2003 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Stat. Sciences
• Author(s): Siddhartha Chib*+
• Companies: Washington University, St. Louis
• Keywords: Bayesian model comparison ; marginal likelihood ; Markov chain Monte Carlo ; semiparametric regression ; smoothness prior

Abstract

We study the problem of comparing alternative Bayesian additive regression models from a fully Bayesian marginal likelihood/Bayes factor perspective. In the approach that is formulated each unknown covariate function is identified by a restriction on the first ordinate and the free ordinates are assigned a proper (second-order) Markov process prior. The model is estimated by Markov chain Monte Carlo (MCMC) simulation techniques. We utilize the MCMC output and the approach of Chib (1995) to provide a straightforward technique to estimate the marginal likelihood. Under the estimation framework of Albert and Chib (1993), the approach is extended to generalized additive regression models for both clustered and nonclustered binary response data, and to models with unobserved confounders. Experiments with simulated and real data demonstrate that the methods perform well, even in high-dimensional settings with several unknown functions.