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The Bernstein-von Mises theorem for semiparametric mixture

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RCL - Representing, calibrating & leveraging prediction uncertainty from statistics to machine learning

Mixture models are a powerful tool for modelling systems with latent variables. Our goal is to estimate some parameter of interest whose distribution depends on some latent variables. Using Bayesian methods, we can find the posterior distribution and get point estimates and uncertainty quantification. However, it is a priori unclear how reliable the Bayesian inference is. With a Bernstein-von Mises theorem we provide a frequentist guarantee for the reliability and asymptotic optimality of the inference. We prove a general BvM theorem and apply it to two specific mixture models: the frailty models and Errors-In-Variables model.

This talk is part of the Isaac Newton Institute Seminar Series series.

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Sackler Lecture Theatre, Level 7 CIMR Room 9, Sidgwick Avenue Lecture Block FW26

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