Statistics Seminar: Vecchia Approximated Bayesian Heteroskedastic Gaussian Processes

Presenter: Parul Patil, Postdoctoral Researcher, UC Santa Cruz

Description: Many computer simulations are stochastic and exhibit input dependent noise. In such situations, heteroskedastic Gaussian processes (hetGPs) make ideal surrogates as they estimate a latent, non-constant variance. However, existing hetGP implementations are unable to deal with large simulation campaigns and use point-estimates for all unknown quantities, including latent variances. This limits applicability to small experiments and undercuts uncertainty. We propose a Bayesian hetGP using elliptical slice sampling (ESS) for posterior variance integration, and the Vecchia approximation to circumvent computational bottlenecks. We show good performance for our upgraded hetGP capability, compared to alternatives, on a benchmark example and a motivating corpus of more than 9-million lake temperature simulations. An open source implementation is provided as bhetGP on CRAN.

About the speaker: Parul Patil is currently working as a post-doctoral researcher with Dr Paul Parker and Dr Sangwon Hyun at University of California, Santa Cruz. She completed her PhD in May 2026 from Virginia Tech. She had previously completed B.Sc. and M.Sc. in Statistics in India. She works with large-scale data, using statistical tools to model complex processes, quantify uncertainty, and uncover patterns. Her work lies at the intersection of statistics and machine learning with ecological applications, focusing on scalable methods for analyzing high-dimensional and spatially structured data.

This seminar is hosted by Professor Yunyi Shen.