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We consider a nonparametric Bayesian approach to estimation and testing for a multivariate monotone density. Instead of following the conventional Bayesian route of putting a prior distribution complying with the monotonicity restriction,…

This is a writeup, with some elaboration, of the talks by the two authors (a physicist and a statistician) at the first PHYSTAT Informal review on January 24, 2024. We discuss Bayesian and frequentist approaches to dealing with nuisance…

This paper studies the problem of testing whether a function is monotone from a nonparametric Bayesian perspective. Two new families of tests are constructed. The first uses constrained smoothing splines, together with a hierarchical…

In this paper, we propose a simple and easy-to-implement Bayesian hypothesis test for the presence of an association, described by Kendall's \tau coefficient, between two variables measured on at least an ordinal scale. Owing to the absence…

Rigorously quantifying the information in high contrast imaging data is important for informing follow-up strategies to confirm the substellar nature of a point source, constraining theoretical models of planet-disk interactions, and…

Partial correlation coefficients are widely applied in the social sciences to evaluate the relationship between two variables after accounting for the influence of others. In this article, we present Bayes Factor Functions (BFFs) for…

Increasingly complex applications involve large datasets in combination with non-linear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take…

We marshall the arguments for preferring Bayesian hypothesis testing and confidence sets to frequentist ones. We define admissible solutions to inference problems, noting that Bayesian solutions are admissible. We give seven weaker…

Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…

Bayes factors represent the ratio of probabilities assigned to data by competing scientific hypotheses. Drawbacks of Bayes factors are their dependence on prior specifications that define null and alternative hypotheses and difficulties…

Bayesian inference is attractive for its coherence and good frequentist properties. However, it is a common experience that eliciting a honest prior may be difficult and, in practice, people often take an {\em empirical Bayes} approach,…

The posterior distribution in a nonparametric inverse problem is shown to contract to the true parameter at a rate that depends on the smoothness of the parameter, and the smoothness and scale of the prior. Correct combinations of these…

Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…

Motivated by the need to analyze large, decentralized datasets, distributed Bayesian inference has become a critical research area across multiple fields, including statistics, electrical engineering, and economics. This paper establishes…

Consider a linear regression model with regression parameter beta and normally distributed errors. Suppose that the parameter of interest is theta = a^T beta where a is a specified vector. Define the parameter tau = c^T beta - t where c and…

In this paper, we consider Bayesian hypothesis testing for the balanced one-way random effects model. A special choice of the prior formulation for the ratio of variance components is shown to yield an explicit closed-form Bayes factor…

Bayesian inference is used to estimate continuous parameter values given measured data in many fields of science. The method relies on conditional probability densities to describe information about both data and parameters, yet the notion…

When combining apparently inconsistent experimental results, one often implements errors on errors. The Particle Data Group's phenomenological prescription offers a practical solution but lacks a firm theoretical foundation. To address…

Bayesian inference is a widely used statistical method. The free energy and generalization loss, which are used to estimate the accuracy of Bayesian inference, are known to be small in singular models that do not have a unique optimal…

We consider the fractional posterior distribution that is obtained by updating a prior distribution via Bayes theorem with a fractional likelihood function, a usual likelihood function raised to a fractional power. First, we analyze the…