A General Bayesian Model for Heteroskedastic Data with Fully Conjugate Full-Conditional Distributions

Paul Parker
Assistant Professor
Statistics, UC Santa Cruz
Professor Sheng Jiang

Join us on Zoom: https://ucsc.zoom.us/j/94536078144?pwd=Q08wSGFwdWdrQXJlRnNZd012d0E5dz09

Models for heteroskedastic data are relevant in a wide variety of applications ranging from financial time series to environmental statistics. However, the topic of modeling the variance function conditionally has not seen near as much attention as modeling the mean. Volatility models have been used in specific applications, but these models can be difficult to fit in a Bayesian setting due to posterior distributions that are challenging to sample from efficiently. In this work, we introduce a general model for heteroskedastic data. This approach models the conditional variance in a hierarchical framework as a function of any desired covariates or random effects. We rely on multivariate log-Gamma distribution theory in order to construct priors that yield fully conjugate full-conditional distributions. Thus, our approach can easily be fit via Gibbs sampling. Furthermore, we extend the model to a deep learning approach that can provide highly accurate estimates for time dependent data, as well as an extension for heavy-tailed data. We illustrate the methodology via three varied applications.

Speaker Bio: Paul is an assistant professor in the Department of Statistics at the University of California, Santa Cruz. He obtained his Ph.D. in Statistics at the University of Missouri, where he was a recipient of the U.S. Census Bureau Dissertation Fellowship, and a recipient of the University of Missouri Population, Education and Health Center Interdisciplinary Doctoral Fellowship. He is broadly interested in modeling dependent data  for a variety of applications including official statistics, social sciences, and ecology. He is also interested in integration of modern machine learning and data science techniques to help improve statistical models.