Related papers: The Lindley paradox in optical interferometry
There are three principle paradigms of statistics: Bayesian, frequentist and information-based inference. Although these paradigms are in agreement in some contexts, the Lindley paradox describes a class of problems, models of unknown…
Jeffreys-Lindley paradox is a case where frequentist and Bayesian hypothesis testing methodologies contradict with each other. This has caused confusion among data analysts for selecting a methodology for their statistical inference tasks.…
This paper discusses the dual interpretation of the Jeffreys--Lindley's paradox associated with Bayesian posterior probabilities and Bayes factors, both as a differentiation between frequentist and Bayesian statistics and as a pointer to…
The Jeffreys-Lindley paradox stands as the most profound divergence between frequentist and Bayesian approaches to hypothesis testing. Yet despite more than six decades of discussion, this paradox remains frequently misunderstood--even in…
In 1957, Lindley published "A statistical paradox" in Biometrika, revealing a fundamental conflict between frequentist and Bayesian inference as sample size approaches infinity. We present a new paradox of a different kind: a conflict…
The Jeffreys-Lindley paradox exposes a rift between Bayesian and frequentist hypothesis testing that strikes at the heart of statistical inference. Contrary to what most current literature suggests, the paradox was central to the Bayesian…
This paper is concerned with the well known Jeffreys-Lindley paradox. In a Bayesian set up, the so-called paradox arises when a point null hypothesis is tested and an objective prior is sought for the alternative hypothesis. In particular,…
The Jeffreys-Lindley paradox displays how the use of a p-value (or number of standard deviations z) in a frequentist hypothesis test can lead to an inference that is radically different from that of a Bayesian hypothesis test in the form…
In the hypothesis testing framework, p-value is often computed to determine rejection of the null hypothesis or not. On the other hand, Bayesian approaches typically compute the posterior probability of the null hypothesis to evaluate its…
We consider the Jeffreys-Lindley paradox from an objective Bayesian perspective by attempting to find priors representing complete indifference to sample size in the problem. This means that we ensure that the prior for the unknown mean and…
We introduce a new class of priors for Bayesian hypothesis testing, which we name "cake priors". These priors circumvent Bartlett's paradox (also called the Jeffreys-Lindley paradox); the problem associated with the use of diffuse priors…
We study the problem of mismatched binary hypothesis testing between i.i.d. distributions. We analyze the tradeoff between the pairwise error probability exponents when the actual distributions generating the observation are different from…
Bayesian and frequentist methods differ in many aspects, but share some basic optimality properties. In practice, there are situations in which one of the methods is more preferred by some criteria. We consider the case of inference about a…
When a photon interferes with itself while traversing a Mach-Zehnder inteferometer, the output port where it emerges is influenced by the phase difference between the interferometer arms. This allows for highly precise estimation of the…
It has long been known that for the comparison of pairwise nested models, a decision based on the Bayes factor produces a consistent model selector (in the frequentist sense). Here we go beyond the usual consistency for nested pairwise…
We analyze the interference of individual photons in a linear-optical setup comprised of two overlapping Mach-Zehnder interferometers joined via a common beam splitter. We show how, in this setup, two kinds of standard interference effects…
The Lutz-Kelker correction is intended to give an unbiased estimate for stellar parallaxes and magnitudes, but it is shown explicitly that it does not. This paradox results from the application of an argument about sample statistics to the…
The ubiquity of optical coherence arising from its importance in everything from astronomy to photovoltaics means that underlying assumptions such as stationarity and ergodicity can become implicit. When these assumptions become implicit,…
The marginalization paradox involves a disagreement between two Bayesians who use two different procedures for calculating a posterior in the presence of an improper prior. We show that the argument used to justify the procedure of one of…
A crucial challenge to the scaling up of linear optical interferometers is the presence of defective optical components resulting from inevitable imperfections in fabrication and packaging. This work presents a method for circumventing such…