Related papers: On the Jeffreys-Lindley's paradox

Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…

The prior distribution on parameters of a sampling distribution is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective which focuses on missing observations as the source of…

The Rician distribution, a well-known statistical distribution frequently encountered in fields like magnetic resonance imaging and wireless communications, is particularly useful for describing many real phenomena such as signal process…

The use of improper priors in the context of Bayesian hierarchical linear mixed models has been studied under the assumption of normality of the random effects. We study the propriety of the posterior under more flexible distributional…

Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…

This thesis presents the strong and weak forms of the Banach-Tarski paradox based on the Hausdorff paradox. It provides modernized proofs of the paradoxes and necessary properties of equidecomposable and paradoxical sets. The historical…

Bayes [Philos. Trans. R. Soc. Lond. 53 (1763) 370--418; 54 296--325] introduced the observed likelihood function to statistical inference and provided a weight function to calibrate the parameter; he also introduced a confidence…

Counterfactual explanations utilize feature perturbations to analyze the outcome of an original decision and recommend an actionable recourse. We argue that it is beneficial to provide several alternative explanations rather than a single…

In the last months, due to the emergency of Covid-19, questions related to the fact of belonging or not to a particular class of individuals (`infected or not infected'), after being tagged as `positive' or `negative' by a test, have never…

This note is an extended review of the book Error and Inference, edited by Deborah Mayo and Aris Spanos, about their frequentist and philosophical perspective on testing of hypothesis and on the criticisms of alternatives like the Bayesian…

Despite their importance in supporting experimental conclusions, standard statistical tests are often inadequate for research areas, like the life sciences, where the typical sample size is small and the test assumptions difficult to…

Bayesian statistics emphasizes the importance of prior distributions, yet finding an appropriate one is practically challenging. When multiple sample results are taken regarding the frequency of the same event, these samples may be…

If a quantum system is prepared and later post-selected in certain states, "paradoxical" predictions for intermediate measurements can be obtained. This is the case both when the intermediate measurement is strong, i.e. a projective…

While Jeffreys priors usually are well-defined for the parameters of mixtures of distributions, they are not available in closed form. Furthermore, they often are improper priors. Hence, they have never been used to draw inference on the…

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…

Every philosophy has holes, and it is the responsibility of proponents of a philosophy to point out these problems. Here are a few holes in Bayesian data analysis: (1) the usual rules of conditional probability fail in the quantum realm,…

Discussion of "Harold Jeffreys's Theory of Probability revisited," by Christian Robert, Nicolas Chopin, and Judith Rousseau, for Statistical Science [arXiv:0804.3173]

We propose a convergence mode for positive Radon measures which allows a sequence of probability measures to have an improper limiting measure. We define a sequence of vague priors as a sequence of probability measures that converges to an…

When performing Bayesian inference, we frequently need to work with conditional probability densities. For example, the posterior function is the conditional density of the parameters given the data. Some might worry that conditional…

Models with intractable likelihood functions arise in areas including network analysis and spatial statistics, especially those involving Gibbs random fields. Posterior parameter es timation in these settings is termed a doubly-intractable…