CAM Colloquium: Dan Kowal, Department of Statistics and Data Science, Cornell University

Location

655 Rhodes Hall

Description

TItle: Monte Carlo inference for semiparametric Bayesian regression

Abstract: Data transformations are essential for broad applicability of parametric regressionmodels. However, for Bayesian analysis, joint inference of the transformation andmodel parameters typically involves restrictive parametric transformations ornonparametric representations that are computationally inefficient andcumbersome for implementation and theoretical analysis, which limits theirusability in practice. We introduce a simple, general, and efficient strategy for jointposterior inference of an unknown transformation and all regression modelparameters. The proposed approach directly targets the posterior distribution ofthe transformation by linking it with the marginal distributions of the independentand dependent variables, and then deploys a Bayesian nonparametric model via theBayesian bootstrap. Crucially, this approach delivers (1) joint posterior consistencyunder general conditions, including multiple model misspecifications, and (2)efficient Monte Carlo (not Markov chain Monte Carlo) inference for thetransformation and all parameters for important special cases. These tools applyacross a variety of data domains, including real-valued, positive, and compactly-supported data. Simulation studies and an empirical application demonstrate theeffectiveness and efficiency of this strategy for semiparametric Bayesian analysiswith linear models, quantile regression, and Gaussian processes. The R packageSeBR is available on CRAN.Paper: https://doi.org/10.1080/01621459.2024.2395586Software documentation: https://drkowal.github.io/SeBR/

Bio: Dan Kowal is Associate Professor in the Department of Statistics and Data Science at Cornell University. His research interests include Bayesian models and algorithms for dependent data, synthesis and imputation of mixed data, and issues related to statistical interpretability and equity. Dr. Kowal’s research has been recognized with a Young Investigator Award from the Army Research Office, the inaugural Blackwell-Rosenbluth Award, and multiple paper and presentation awards.