Bayesian nonparametric analysis of conditional distributions and inference for Poisson point processes.

摘要

This thesis provides a suite of flexible and practical nonparametric Bayesian analysis frameworks, together related under a particular approach to Dirichlet process (DP) mixture modeling based on joint density estimation with well chosen kernels and inference through finite stick-breaking approximation to the random mixing measure. Development of a novel nonparametric mean regression estimator serves as an introduction to a general modeling approach for nonparametric analysis of conditional distributions through initial inference about joint probability distributions. Three novel regression modeling frameworks are proposed: quantile regression, hidden Markov switching regression, and regression for survival data. A related approach is adopted in modeling for marked spatial Poisson processes. This class of models is then expanded to a full nonparametric framework for inference about marked or unmarked dynamic spatial Poisson processes which occur at discrete time intervals. This involves the development of a version of the dependent DP as a prior on the space of correlated sets of probability distributions. Posterior simulation methodology is contained throughout and numerous data examples have been provided in illustration.