Related papers: The Lindley paradox in optical interferometry
Hardy's paradox is analysed within Feynman's formulation of quantum mechanics. A transition amplitude is represented as a sum over virtual paths which different intermediate measurements convert into different sets of real pathways.…
Variational Bayesian posterior inference often requires simplifying approximations such as mean-field parametrisation to ensure tractability. However, prior work has associated the variational mean-field approximation for Bayesian neural…
Measures of association in contingency tables, such as odds ratios and their generalizations, are often studied under different sampling schemes that either fix or leave random the margins of the table. While classical results show that…
Bertrand's paradox is a famous problem of probability theory, pointing to a possible inconsistency in Laplace's principle of insufficient reason. In this article we show that Bertrand's paradox contains two different problems: an "easy"…
Meta-analysis is an important tool for combining results from multiple studies and has been widely used in evidence-based medicine for several decades. This paper reports, for the first time, an interesting and valuable paradox in…
Extraneous motion of optical elements in an interferometer lead to excess noise. Typically, fluctuations in the effective path length lead to phase noise, while beam-pointing leads to apparent amplitude noise. For a transmissive optic…
In many hypothesis testing applications, we have mixed priors, with well-motivated informative priors for some parameters but not for others. The Bayesian methodology uses the Bayes factor and is helpful for the informative priors, as it…
We study the number of coincidences in a Hong-Ou-Mandel interferometer exit whose arms have been supplemented with the addition of one or two optical cavities. The fourth-order correlation function at the beam-splitter exit is calculated.…
A simple classical, deterministic, local situation violating the Bell inequality is described. The detectors used in the experiment are ideal and the observers who decide which pair of measuring devices to choose for a given pair of…
Bayesian model averaging, model selection and its approximations such as BIC are generally statistically consistent, but sometimes achieve slower rates og convergence than other methods such as AIC and leave-one-out cross-validation. On the…
We use a photon-number resolving detector to monitor the photon number distribution of the output of an interferometer, as a function of phase delay. As inputs we use coherent states with mean photon number up to seven. The postselection of…
Optical lossless beam splitters are frequently encountered in fundamental physics experiments regarding the nature of light, including "which-way" determination of light particles, N. Bohr's complementarity principle, or the EPR paradox and…
A key sticking point of Bayesian analysis is the choice of prior distribution, and there is a vast literature on potential defaults including uniform priors, Jeffreys' priors, reference priors, maximum entropy priors, and weakly informative…
In this paper, I will demonstrate a new perspective on the Two Envelope Problem. I hope to show with convincing clarity how the paradox results from an inherent problem pertaining to the interpretation of Bayesian probability. Specifically,…
Different ways of extracting parameters of interest from combined data sets of separate experiments are investigated accounting for the systematic errors. It is shown, that the frequentist approach may yield larger $\chi^2$ values when…
We revisit the flatland paradox proposed by \cite{ston1976} which is an example of non-conglomerability. The aim of the paper is to show that the improperness of the prior is not directly involved in the inconsistency. First, we show that…
In this paper we propose a Bayesian answer to testing problems when the hypotheses are not well separated. The idea of the method is to study the posterior distribution of a discrepancy measure between the parameter and the model we want to…
This paper deals with a new Bayesian approach to the standard one-sample $z$- and $t$- tests. More specifically, let $x_1,\ldots,x_n$ be an independent random sample from a normal distribution with mean $\mu$ and variance $\sigma^2$. The…
When using complex Bayesian models to combine information, the checking for consistency of the information being combined is good statistical practice. Here a new method is developed for detecting prior-data conflicts in Bayesian models…
In order to estimate model parameters and circumvent possible difficulties encountered with the likelihood function, we propose to replace the likelihood in the formula of the posterior distribution by a function depending on a contrast.…