Events

Bayesian inference using mixed Laplace approximation with applications to error-in-operator models

Speaker: Vladimir Spokoiny

Location: 60 Fifth Avenue, Room 650

Date: Tuesday, October 3, 2023

Many statistical problems can be viewed as an error-in-operator model when a linear operator is not known precisely. Examples include random design regression, stochastic diffusion, error-in-variables regression, instrumental variable regression, functional data analysis, Markov chain prediction, interacting particle systems, among many others.

We consider the Bayesian inference problem for such models in a unified way. The key step of the analysis is a mixed Laplace approximation which states an approximation of a high dimensional posterior by a mixture of Gaussians. We also provide sufficient conditions in terms of effective parameter dimension when the mixture of Gaussian can be replaced by one Gaussian distribution.

The results will be illustrated for the case of high dimensional random design regression.