A0575
Title: Unified Bayesian nonparametric framework for ordinal, survival, and density regression using complementary log-log link
Authors: Entejar Alam - University of Texas at Austin (United States) [presenting]
Antonio Linero - University of Texas at Austin (United States)
Abstract: Applications of the complementary log-log (cloglog) link to problems in Bayesian nonparametrics are developed. Although less commonly used than the probit or logit links, it is found that the cloglog link is computationally and theoretically well-suited to several commonly used Bayesian nonparametric methods. The starting point is a Bayesian nonparametric model for ordinal regression. It is first reviewed how the cloglog link uniquely sits at the intersection of the cumulative link and continuation ratio approaches to ordinal regression. Then, a convenient computational method is developed for fitting these ordinal models using Bayesian additive regression trees. Next, the ordinal regression model is used to build a Bayesian nonparametric stick-breaking process and show that, under a proportional hazards assumption, the stick-breaking process can be used to construct a weight-dependent Dirichlet process mixture model. Again, Bayesian additive regression trees lead to convenient computations. These models are then extended to allow for Bayesian nonparametric survival analysis in both discrete and continuous time. The models have desirable theoretical properties, and this is illustrated by analyzing the posterior contraction rate of the ordinal models. Finally, the practical utility of the cloglog models is demonstrated through a series of illustrative examples.
