The Bayes Estimator of a Conditional Density: Consistency

TL;DR

This paper proves that within a Bayesian framework, the optimal estimator for a conditional density converges to the true density as data increases, establishing its consistency.

Contribution

It provides a theoretical proof of the consistency of the Bayes estimator for conditional densities, a foundational result in Bayesian nonparametrics.

Findings

The Bayes estimator is consistent for conditional densities.

The proof relies on Bayesian convergence principles.

This result supports the use of Bayesian methods for density estimation.

Abstract

In a Bayesian framework we prove that the optimal estimator of a conditional density is consistent.