  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.
