Bayesian adaptation

TL;DR

This paper explores Bayesian adaptive estimation methods that use priors independent of the function's regularity or sample size, aiming for minimax-optimal rates in infinite-dimensional problems.

Contribution

It clarifies the relationships among various prior design approaches for minimax-optimal adaptive estimation in infinite-dimensional settings.

Findings

Identifies key principles behind prior design for adaptive estimation

Provides insights into the relationship between different Bayesian approaches

Highlights the importance of prior independence from regularity and sample size

Abstract

In the need for low assumption inferential methods in infinite-dimensional settings, Bayesian adaptive estimation via a prior distribution that does not depend on the regularity of the function to be estimated nor on the sample size is valuable. We elucidate relationships among the main approaches followed to design priors for minimax-optimal rate-adaptive estimation meanwhile shedding light on the underlying ideas.