Prior Processes and Their Applications ― Nonparametric Bayesian Estimation

This book presents a systematic and comprehensive treatment of various prior processes that have been developed over the last four decades in order to deal with the Bayesian approach to solving some nonparametric inference problems. Applications of these priors in various estimation problems are presented. Starting with the famous Dirichlet process and its variants, the first part describes processes neutral to the right,gamma and extended gamma, beta and beta-Stacy, tailfree and Polya tree, one and two parameter Poisson-Dirichlet, the Chinese Restaurant and Indian Buffet processes, etc., and discusses their interconnection. In addition, several new processes that have appeared in the literature in recent years and which are offshoots of the Dirichlet process are described briefly. The second part contains the Bayesian solutions to certain estimation problems pertaining to the distribution function and its functional based on complete data. Because of the conjugacy property of these processes, most of these solutions are inclosed form. The third part treats similar problems but based on right censored data. Other applications are also included. A comprehensive list of references is provided in order to help readers explore further on their own.

Eswar Phadia received his doctorate from Ohio State University and has been on the faculty of William Paterson University of New Jersey for nearly four decades, during which he has served as Chairman of the Department, Director of Research and Dean of the College of Science and Health. He has published numerous papers in the areas of Nonparametric Bayesian Inference, Survival Analysis, and Decision Theory in scientific journals including the Annals of Statistics. He has been the recipient of several NSF grants, State grants and University awards. He was a visiting faculty/scholar at UCLA, Harvard, UC, Davis, and spent sabbaticals at Rutgers, Columbia and the University of Pennsylvania. He has presented papers at professional meetings nationally and internationally and has given seminars and lectures in the United States and in Canada, China, India, Jordan and Singapore. He is a member of the Institute of Mathematical Statistics, the American Statistical Association and an elected member of the International Statistical Institute.