DMS Colloquium: Dr. Lu Zhang

Speaker: Dr. Lu Zhang, University of Southern California

Title: Bayesian inference for high-dimensional latent spatial model—Why we should and how to avoid random walk in MCMC

Abstract: High-dimensional latent spatial process models can present a significant challenge when it comes to obtaining Bayesian inference. In this talk. we will explore the pathological geometry features of the posterior distribution of latent spatial process models that impede the efficiency of MCMC sampling. I will present our proposed solutions that use conjugate and conditional conjugate prior along with scalable spatial modeling techniques to facilitate posterior sampling and posterior prediction. Our approaches exploit distribution theory for the Matrix-Normal distribution, which we use to construct scalable versions of a hierarchical linear model of coregionalization (LMC) and spatial factor models that deliver inference over a high-dimensional parameter space including the latent spatial process. Additionally, we develop Bayesian predictive stacking of spatial process models for geostatistical applications, which extends the prediction performance of conjugate spatial models. Our findings will be demonstrated through simulation studies and analyses of a large vegetation index data set, highlighting the computational and inferential benefits of our approaches compared to competing methods.

Short Bio: Lu Zhang is an Assistant Professor in the Division of Biostatistics in the Department of Population and Public Health Sciences at Keck School of Medicine, University of Southern California (USC). Prior to joining USC, she worked as a postdoctoral researcher with Andrew Gelman in the Department of Statistics at Columbia University, and with Bob Carpenter from Flatiron Institute. In 2020, she received her doctoral degree in Biostatistics under the supervision of Sudipto Banerjee from the Department of Biostatistics at University of California, Los Angeles (UCLA). Her research interests include statistical modeling and analysis for geographically referenced data, Bayesian statistics (theory and methods), statistical computing, and related software development.

Faculty host: Haoran Li