Related papers: Bayes Factors for Peri-Null Hypotheses

Equivalence tests, otherwise known as parity or similarity tests, are frequently used in ``bioequivalence studies" to establish practical equivalence rather than the usual statistical significant difference. In this article, we propose an…

Given the well-known and fundamental problems with hypothesis testing via classical (point-form) significance tests, there has been a general move to alternative approaches, often focused on the Bayesian t-test. We show that the Bayesian…

Bayesian and frequentist criteria fundamentally differ, but often posterior and sampling distributions agree asymptotically (e.g., Gaussian with same covariance). For the corresponding single-draw experiment, we characterize the frequentist…

In Bayesian statistics, one's prior beliefs about underlying model parameters are revised with the information content of observed data from which, using Bayes' rule, a posterior belief is obtained. A non-trivial example taken from the…

Measures of association play a central role in the social sciences to quantify the strength of a linear relationship between the variables of interest. In many applications researchers can translate scientific expectations to hypotheses…

Loss-based updating, including generalized Bayes, Gibbs, and quasi-posteriors, replaces likelihoods by a user-chosen loss and produces a posterior-like distribution via exponential tilt. We give a decision-theoretic characterization that…

Bayesian tests on the symmetry of the generalized von Mises model for planar directions (Gatto and Jammalamadaka, 2007) are introduced. The generalized von Mises distribution is a flexible model that can be axially symmetric or asymmetric,…

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,…

Gaussian empirical Bayes methods usually maintain a precision independence assumption: The unknown parameters of interest are independent from the known standard errors of the estimates. This assumption is often theoretically questionable…

Bayes factors, in many cases, have been proven to bridge the classic -value based significance testing and bayesian analysis of posterior odds. This paper discusses this phenomena within the binomial A/B testing setup (applicable for…

We propose a new method for conducting Bayesian prediction that delivers accurate predictions without correctly specifying the unknown true data generating process. A prior is defined over a class of plausible predictive models. After…

We study the posterior distribution of the Bayesian multiple change-point regression problem when the number and the locations of the change-points are unknown. While it is relatively easy to apply the general theory to obtain the…

When interpreting A/B tests, we typically focus only on the statistically significant results and take them by face value. This practice, termed post-selection inference in the statistical literature, may negatively affect both point…

Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…

Hypothesis testing results often rely on simple, yet important assumptions about the behaviour of the distribution of p-values under the null and the alternative. We examine tests for one dimensional parameters of interest that converge to…

A number of biomedical problems require performing many hypothesis tests, with an attendant need to apply stringent thresholds. Often the data take the form of a series of predictor vectors, each of which must be compared with a single…

Bayesian inference provides a natural framework for updating knowledge as new information becomes available, often in a sequential manner by incorporating datasets in stages or reusing previous posteriors as priors. In practice, this is…

The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…

Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…

A common task in physics and astronomy is studying which of the competing hypotheses the data prefer. This is usually done by computing the Bayes factor between the two hypotheses, and either interpreting it in terms of the posterior odds…