This thesis presents three applications of Bayesian nonparametric in econo-metric models. The models we consider include flexible discrete choice models, mixture of autoregressive models and mixed proportional hazard models. These three models can be written in the mixture forms. The unknown mixing distri-bution is assumed to be the Ferguson (1973)'s Dirichlet process prior. For the mixed proportional hazard models, the baseline hazard rate is further assumed to be a mixture of the weighted gamma process prior. The posterior distributions of the Dirichlet process, the weighted gamma process and the marginal distribution of the augmented variables can be derived by the applications of Lo (1984) dis-integration/Fubini theorem and Lo and Weng (1989) and James (2003) weighted gamma process...[ Read more ]

This thesis presents three applications of Bayesian nonparametric in econo-metric models. The models we consider include flexible discrete choice models, mixture of autoregressive models and mixed proportional hazard models. These three models can be written in the mixture forms. The unknown mixing distri-bution is assumed to be the Ferguson (1973)'s Dirichlet process prior. For the mixed proportional hazard models, the baseline hazard rate is further assumed to be a mixture of the weighted gamma process prior. The posterior distributions of the Dirichlet process, the weighted gamma process and the marginal distribution of the augmented variables can be derived by the applications of Lo (1984) dis-integration/Fubini theorem and Lo and Weng (1989) and James (2003) weighted gamma process calculus. All posterior quantities can be represented in terms of partitions. The partition representation is a Rao-Blackwellization of the aug-mented variables representation. In practice, the recent algorithms, Lo, Bunner and Chan (1996)'s weighted chinese restaurant process and Ishwaran and James (2001, 2003)'s Blocked Gibbs Sampler, are employed to evaluate the posterior distributions. Simulation studies and real data analysis are also presented.<sup>1

1</sup> Section 2 Flexible Choice Modeling based on Bayesian Nonparametric Mixed Multinomial Logit Models is done with Prof. James, Lancelot, Section 3 Mixture of Autoregressive Model is done with Prof. So, Mike K. P. and Section 4 Bayesian Nonparametric Modeling for Mixed Proportional Hazard Models with Right Censoring is done by the author only.