Organizer:

Siddhartha Chib, chib@simon.wustl.edu

Speakers

8:15 a.m.
Fully Model Based Approaches for Spatially Misaligned Data
Bradley Carlin, University of Minnesota

8:40 a.m.
Weighted Monte Carlo Estimates For Computing Posterior Quantities
Ming-Hui Chen, Worcester Polytechnic Institute (with Qi-Man Shao)

Although various efficient and sophisticated Markov chain Monte Carlo sampling methods have been developed during the last decade, the sample mean is still a dominated Monte Carlo estimate used in computing Bayesian posterior quantities. The sample mean estimate is simple, but not efficient. The weighted Monte Carlo estimate is a natural generalization of the sample mean estimate. A brief overview of the weighted estimates will be provided. The general strategies of how to construct good weights will be discussed. An interesting theoretical finding along with some preliminary simulation study will be presented.

9:05 a.m.
Simulation Based Optimal Design and some Applications in Clinical Trials
Peter Mueller, Duke University (with Don Berry)
Keywords: backward induction, forward simulation, Monte Carlo simulation, optimal design, sequential decision

We discuss simulation based methods for exploration and maximization of expected utility in sequential decision problems. We consider problems which require backward induction with analytically intractable expected utility integrals at each stage. We propose to use forward simulation to approximate the integral expressions, and a reduction of the allowable action space to avoid problems related to an exponentially exploding number of possible trajectories in the backward induction. The artificially reduced action space allows strategies to depend on the full history of earlier observations and decisions only indirectly through a low dimensional summary statistic. We illustrate the proposed approach with an application to an optimal stopping problem in a clinical trial.

9:30 a.m.
Analysis of Cross-Section and Clustered Data Treatment Models
Siddhartha Chib, Washington University at St. Louis (with Barton Hamilton)
Keywords: causal inference; categorical treatments; finite mixture distribution; Gibbs sampling; Markov chain Monte Carlo; non-experimental data; potential outcomes; randomly assigned covariate; sample selection; treatment effect

This paper is concerned with the problem of determining the effect of a categorical treatment variable on a response given that the treatment is non-randomly assigned and the response (on any given subject) is observed for one setting of the treatment. We consider classes of models that are designed for such problems. These models are subjected to a fully Bayesian analysis based on Markov chain Monte Carlo methods. The analysis of the treatment effect is then based on, amongst other things, the posterior distribution of the potential outcomes (counter-factuals) at the subject level, which is obtained as a by-product of the MCMC simulation procedure. The analysis is extended to models with categorical treatments and binary and clustered outcomes. The problem of model comparisons is also considered. Different aspects of the methodology are illustrated through two data examples.