I have been interested in what happens when Bayesian analysis meets nonparametric models. Mike Escobar, Steve MacEachern, Mike West, Peter Muller, Hani Doss and others have showed how to design Monte Carlo codes to simulate posterior distributions in this context. One of my contributions is an approximate recursive algorithm to speed up some of these calculations.

Papers in the area

• M.A. Newton , 1994. A diffuse prior limit in semiparametric binary regression. American Statistical Association Proceedings of the Section on Bayesian Statistical Science , 181--186. Also UW Madison Department of Statistics Technical Report 936.
• M.A. Newton , C. Czado, and R. Chappell, 1996. Bayesian inference for semiparametric binary regression. Journal of the American Statistical Association, 91, 142-153.
• M.A. Newton , and Y. Zhang (1999). A recursive algorithm for nonparametric analysis with missing data. Biometrika, 86 , 15-26.
• M.A. Newton , F.A. Quintana, and Y. Zhang (1998). Nonparametric Bayes methods using predictive updating. In Practical nonparametric and semiparametric Bayesian statistics (eds D. Dey, P. Muller, and D. Sinha), pp 45-61. New York: Springer.
• Huageng Tao, Mari Palta, Brian S. Yandell, and M. A. Newton (1999). An estimation method for the semiparametric mixed effects model. Biometrics, 55 , 199-202.

• M.A. Newton. On a nonparametric recursive estimator of the mixing distribution. Sankhya Series A. 64 1-17. (See also UW Statistics TR #1021).

Splus/R code

• .tar.gz R package to do semiparametric binary regression as in Newton, Czado, and Chappell 1996. By Alejandro.JaraVallejos@med.kuleuven.be. Thanks!
• Censored data example [from Newton et al 1998]
• Binomial mixtures example [from Newton et al 1998]