Bayesian Quantile Regression and its Applications

Subhashis Ghoshal

North Carolina State University
Barton Lectures in Computational Mathematics


Date: Wednesday, November 2, 2022
Time: 3:30 pm - 5:00 pm
Location: Petty 150
Subhashis Ghoshal is the Goodnight Distinguished Professor of Statistics at the Department of Statistics of North Carolina State University (NCSU), Raleigh, NC, where he has been working since 2001. He got his Ph.D. in Statistics from the Indian Statistical Institute in 1995. His current research interests include Bayesian nonparametrics, high-dimensional statistics, graphical models, shape-restricted inference, functional data, differential equation models, image processing, and biomedical applications. He has published over 125 papers. He has been very well cited, especially for his papers developing the theory of posterior convergence rates. He is a fellow of the Institute of Mathematical Statistics (IMS), the American Statistical Association (ASA), and the International Society for Bayesian Analysis (ISBA), and received the International Indian Statistical Association (IISA) Young Researcher Award in Theory and Methodology in 2007. He also won the prestigious De Groot Prize in 2019 for the best book in Statistical Sciences from the ISBA. His research has been supported by grants from the National Science Foundation including its CAREER Award, Army Research Office, National Security Agency, Samsung Electronics, Office of Naval Research, and several European Agencies. He also obtained funding to support the travel costs of many young researchers to attend several conferences he was associated with. He held honorary positions as the Eurandom Chair Professor, Eindhoven, The Netherlands, and the Royal Netherlands Academy of Arts and Sciences Visiting Professorship, Leiden University. Thus far, thirty doctoral students graduated under his guidance. He was awarded the Cavell Brownie Mentoring Award by the Department of Statistics of NCSU. He is currently serving, or has served, on the editorial boards of many top statistics journals, grant panels, scientific committees of several major statistics conferences, and organized two major international statistics conferences at his department. He is presently the past chair of the Bayesian nonparametric section of ISBA and the president elect of the IISA.

A primary driving force behind learning is discovering relationships between variables of interest. Most relationships in the real world are not perfect, therefore finding them needs using regression analysis, a statistical tool. The relation between the mean of the response variable and the predictor variable is frequently described by a regression curve. However, if the main focus is on exceptional events, such a description may provide an inadequate view of the response variables’ variability as the predictor variable changes. If the distribution of the response variable, such as income or housing prices, is considerably skewed, mean regression is also inappropriate since only a small subset of values can significantly alter the behavior of the mean. Different relations can occur at various quantile levels in quantile regression. In this session, we take into account a simultaneous Bayesian approach to quantile regression for all quantile levels. With this method, we use a prior probability distribution to describe the uncertainty in the unknown quantities and then update it to a posterior probability distribution to draw conclusions after observing the data. We use a B-spline basis to expand the quantile function and assign a suitable prior distribution on the coefficients while taking into account the inherent ordering among quantiles. We use the method to examine data on internal migrations in the US over time as well as data on Atlantic storms. The method is then extended to spatio-temporal data by expanding quantiles in a basis of tensor products of B-splines. We use this to analyze a dataset on US ground-level ozone pollution. Finally, we discuss a purely nonparametric method that avoids the linearity assumption between quantiles and the predictor variable. We apply it to study the evolution of US household income across races and income levels over time.