A0722
Title: On posterior mixing under unidentified nonparametric models
Authors: Chong Zhong - The Hong Kong Polytechnic University (Hong Kong) [presenting]
Jin Yang - The Hong Kong polytechnic University (Hong Kong)
Junshan Shen - Capital Univeristy of Economics and Business (China)
Catherine Liu - The Hong Kong Polytechnic University (Hong Kong)
Zhaohai Li - Geoge Washington University (United States)
Abstract: Poor mixing is a stumbling block to Bayesian prediction under nonparametric models with multiple unidentified infinite dimensional parameters, incurring poor estimation of the posterior predictive distribution. Motivated by the prediction under unidentified transformation models, we address poor mixing through a criterion that quantifies the informativeness of nonparametric priors to help the sampler correctly explore the posterior. We first recast the transformation model to its equivalence with a compressed parameter space and propose a set of nonparametric priors. Under general conditions, we formulate the relationship between the asymptotic posterior variation and the nonparametric priors, allowing people to adjust the informativeness of nonparametric priors to fulfill the criterion to obtain mixed posterior. We also find an interesting result that the posterior is still proper even if the prior for the finite-dimensional parameter is improper. Comprehensive simulations and real-world data analysis illustrate our method in addressing poor mixing and demonstrate the superiority in predicting survival outcomes compared with contemporary methods.
