The Lindley paradox in optical interferometry

TL;DR

This paper explores the Lindley paradox in optical interferometry, highlighting how Bayesian and frequentist methods diverge in phase estimation, and proposes priors to reconcile these differences for better high-precision measurements.

Contribution

It investigates the Lindley paradox in optical interferometry and offers strategies to mitigate the conflict between Bayesian and frequentist approaches.

Findings

Identifies conditions where the Lindley paradox occurs in optical phase estimation

Demonstrates how prior choices influence hypothesis testing outcomes

Proposes methods to align Bayesian and frequentist results in interferometry

Abstract

The so-called Lindley paradox is a counterintuitive statistical effect where the Bayesian and frequentist approaches to hypothesis testing give radically different answers, depending on the choice of the prior distribution. In this paper we address the occurrence of the Lindley paradox in optical interferometry and discuss its implications for high-precision measurements. In particular, we focus on phase estimation by Mach-Zehnder interferometers and show how to mitigate the conflict between the two approaches by using suitable priors.