Iterative simulations such as Markov chain Monte Carlo (MCMC) have made it possible to fit complex and more realistic Bayesian models to large and/or incomplete datasets. However, there are still many open questions in using (MCMC) methods. Our research program in this field features the following aspects:

1. (Over-dispersed) Starting Distribution and Convergence Diagnostics

   Gelman and Rubin (1992) noticed the importance of running multiple MCMC chains for obtaining reliable statistical inferences. Chuanhai Liu and Donald B. Rubin are continuing their work on "Markov Analysis of Iterative Simulations Before Their Convergence" (Liu and Rubin, 1996), which can be used to create an overdispersed starting distribution for running multiple chains.

2. Efficient MCMC Algorithms

   We have developed several efficient MCMC algorithms:

   • the Monotone Data Augmentation algorithm, proposed by Rubin and Schafer (1990), for multiple imputation, extensively studied by Chuanhai Liu and his coauthors (Liu and Rubin, 1998; Gelman, King, and Liu, 1998), and
   • focused sampling methods, developed by Mark Hansen and his coauthors (Wong, Hansen, Kohn, and Smith, 1998).

3. Applications

   MCMC methods have been applied to many projects within the Statistical Research Department at Bell Labs. For example,

   • Bayesian models for the CVA project (Clark et al, 1998);
   • Bayesian models for analysis of rating scale data (Cleveland and Liu, 1998);
   • Analysis of censored data from fractionated experiments using covariance adjustments (Liu and Sun, 1998);
   • Nonparametric and robust regression (Wong, Hansen, Kohn, and Smith, 1998); and
   • Analysis of incomplete data and multiple imputation .