RKL: a general, invariant Bayes solution for Neyman-Scott

TL;DR

This paper introduces RKL, a general invariant Bayes estimator that guarantees consistency for the Neyman-Scott problem and extends to broader estimation scenarios, addressing limitations of previous methods.

Contribution

It proposes a simple, invariant Bayes estimator that ensures consistency for Neyman-Scott and generalizes to other estimation problems, overcoming prior ad-hoc solutions.

Findings

The estimator is invariant to representation.

It guarantees consistency for Neyman-Scott.

It generalizes beyond Neyman-Scott.

Abstract

Neyman-Scott is a classic example of an estimation problem with a partially-consistent posterior, for which standard estimation methods tend to produce inconsistent results. Past attempts to create consistent estimators for Neyman-Scott have led to ad-hoc solutions, to estimators that do not satisfy representation invariance, to restrictions over the choice of prior and more. We present a simple construction for a general-purpose Bayes estimator, invariant to representation, which satisfies consistency on Neyman-Scott over any non-degenerate prior. We argue that the good attributes of the estimator are due to its intrinsic properties, and generalise beyond Neyman-Scott as well.