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	Exact Sampling of Gibbs Measures with Estimated Losses

Host: Prof. Pivkin, Prof. Sulem

Tuesday

11.02

USI East Campus, Room D5.01

12:00-13:00


	Jack Jewson Monash University

Abstract: In recent years, the shortcomings of Bayesian posteriors as inferential devices have received increased attention. A popular strategy for fixing them has been to instead target a Gibbs measure based on losses that connect a parameter of interest to observed data. However, existing theory for such inference procedures assumes these losses are analytically available, while in many situations these losses must be stochastically estimated using pseudo-observations. In such cases, we show that when standard Markov Chain Monte Carlo algorithms are used to produce posterior samples, the resulting posterior exhibits a strong dependence on the number of pseudo-observations: unless the number of pseudo-observations diverge sufficiently fast the resulting posterior will concentrate very slowly. However, we show that in certain situations it is feasible to alleviate this dependence entirely using modified versions of piecewise deterministic Markov process (PDMP) samplers, and we formally and empirically show that these samplers produce posterior draws that have no dependence on the number of pseudo-observations used to estimate the loss within the Gibbs Measure. We apply our results to three Gibbs measures that have been proposed to deal with intractable likelihoods and model misspecification by Cherief Abdellatif and Alquier (2020) and Alquier and Gerber (2024).

Biography: Jack is a Senior Lecturer in the Department of Econometrics and Business Statistics at Monash University, Melbourne, Australia. Jack's research focuses on methodological and computational challenges in modern Bayesian Inference. Particular areas of interest include Model Misspecification, Robustness, Inference with Loss Functions, and Variable/Model Selection