CCM Colloquium: Jonathan Huggins (Boston University)Event

Wednesday Oct 9, 2024, 10:00 AM → 11:00 AM America/New_York

3rd floor classroom (162)

Presenter: Jonathan Huggins (Boston University)

Title: Gaussian Process Surrogates for Bayesian Inverse Problems

Abstract: In scientific applications, we frequently encounter statistical models that require running expensive computer simulations, often in the form of numerically solving systems of (possibly stochastic) differential equations. When solving the Bayesian inverse problem of inferring the parameters of these models, standard posterior inference algorithms are infeasible since only a small number of simulations, and thus log likelihood evaluations, can be performed. One popular solution is to run the simulator (often in parallel) on a carefully selected set of parameter values, then use these evaluations to build a predictive model for either the simulator output or the model log-likelihood. That predictive model, which by design is fast to evaluate, can then be used as a surrogate to approximate the log likelihood. Gaussian processes (GPs) are a popular choice of surrogate, and many approaches to using GPs have been proposed and analyzed. In this talk, I’ll outline some preliminary steps towards a framework for (a) conceptualizing the design space of surrogate-based posterior inference algorithms, (b) determining how best to incorporate GP uncertainty in the posterior approximation, and (c) designing effective criteria for sequentially selecting the parameter values at which to evaluate the exact log likelihood. Throughout the talk, I’ll illustrate the importance of these issues in an application to modeling the terrestrial carbon cycle, which is important for climate forecasting and ecosystem management.