Related papers: The Lindley paradox in optical interferometry
The four Rindler quadrants of a pair of oppositely accelerated frames are identified as a (Lorentzian) Mach-Zehnder interferometer. The Rindler frequency dependence of the interference process is expressed by means of a (Lorentzian)…
The focal-loss has become a widely used alternative to cross-entropy in class-imbalanced classification problems, particularly in computer vision. Despite its empirical success, a systematic information-theoretic study of the focal-loss…
The discrepant posterior phenomenon (DPP) is a counter-intuitive phenomenon that can frequently occur in a Bayesian analysis of multivariate parameters. It refers to the phenomenon that a parameter estimate based on a posterior is more…
Study of the bivariate normal distribution raises the full range of issues involving objective Bayesian inference, including the different types of objective priors (e.g., Jeffreys, invariant, reference, matching), the different modes of…
The phase uncertainty of an unseeded nonlinear interferometer, where the output of one nonlinear crystal is transmitted to the input of a second crystal that analyzes it, is commonly said to be below the shot-noise level but highly…
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…
In latent variable models the parameter estimation can be implemented by using the joint or the marginal likelihood, based on independence or conditional independence assumptions. The same dilemma occurs within the Bayesian framework with…
In this paper we compare the performance of multi and single-mode interferometry for the estimation of the phase of the complex visibility. We provide a theoretical description of the interferometric signal which enables to derive the phase…
A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in…
We consider whether the asymptotic distributions for the log-likelihood ratio test statistic are expected to be Gaussian or chi-squared. Two straightforward examples provide insight on the difference.
A coherent account of the connections and contrasts between the principles of com- plementarity and uncertainty is developed starting from a survey of the various formalizations of these principles. The conceptual analysis is illustrated by…
It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings…
Interference effects are usually observed by intensity measurement. Path indistinguishability by quantum complementarity principle requires projection of the interfering fields into a common indistinguishable mode before detection. On the…
Interim analyses are vital in clinical trials for early decision-making. While frequentist implications are well-established, the consequences of repeated Bayesian interim monitoring for efficacy, specifically regarding multiplicity, remain…
The Tolman paradox is well known as a base for demonstrating the causality violation by faster-than-light signals within special relativity. It is constructed using a two-way exchange of faster-than-light signals between two inertial…
In this work we investigate the problem of simultaneous estimation of phases using generalised three- and four-mode Mach-Zehnder interferometer. In our setup, we assume that the phases are placed in each of the modes in the interferometer,…
Local sensitivity diagnostics for Bayesian models are described that are analogues of frequentist measures of leverage and influence. The diagnostics are simple to calculate using MCMC. A comparison between leverage and influence allows a…
Inserting a lossy dielectric into one arm of an interference experiment acts in many ways like a measurement. If two entangled photons are passed through the interferometer, a certain amount of information is gained about which path they…
Standard statistical theory has arguably proved to be unsuitable as a basis for constructing a satisfactory completely general framework for performing statistical inference. For example, frequentist theory has never come close to providing…
Interferometry has been used widely in sensing application. However, the technique is limited by the finite coherence time of the light sources when the interference paths are not balanced. Higher-order interference effects involve…