The Lindley paradox in optical 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.

Prospects for LISA to detect a gravitational-wave background from first order phase transitions

“…The sensitivity of the Bayes factor to the choice of increasingly diffuse priors is well known and often referred to as Lindley's paradox [61,62]. It is illustrated for instance in [63] for an example of a Gaussian likelihood with unknown mean θ and unknown variance σ 2 where a Normal(0,τ 2 ) prior is put on the variance parameter σ 2 . With increasing τ 2 , the marginal likelihood of the null model θ = θ 0 and that of the alternative will converge to 1 and zero, respectively, no matter the value of the data.…”