Statistics Department Seminar Series: Maria DeYoreo, Ph.D., Department of Statistical Science, Duke University

Abstract:

I introduce a Bayesian nonparametric framework for modeling ordinal regression relationships which evolve in discrete time. The motivating application involves a key problem in fisheries research on estimating relationships between age, length and maturity (recorded on an ordinal scale), across time. The methodology builds from nonparametric mixture modeling for the joint stochastic mechanism of covariates and latent continuous responses. This approach yields flexible inference for ordinal regression functions while at the same time avoiding challenges present in parametric models. A novel dependent Dirichlet process prior for time-dependent mixing distributions extends the model to the dynamic setting. The methodology is applied to study relationships between maturity, age, and length for Chilipepper rockfish, using data collected over 15 years along the coast of California. I also outline related methodology for effectively handling missing values in heterogeneous data, and discuss current work on data fusion and integration.