Related papers: Bayesian hypothesis tests with diffuse priors: Can…
The Bayesian evidence is a key tool in model selection, allowing a comparison of models with different numbers of parameters. Its use in analysis of cosmological models has been limited by difficulties in calculating it, with current…
A family of random probabilities is defined and studied. This family contains the Dirichlet process as a special case, corresponding to an inner point in the appropriate parameter space. The extension makes it possible to have random means…
In this article, we consider the problem of simultaneous testing of hypotheses when the individual test statistics are not necessarily independent. Specifically, we consider the problem of simultaneous testing of point null hypotheses…
To the frequentist who computes posteriors, not all priors are useful asymptotically: in this paper Schwartz's 1965 Kullback-Leibler condition is generalised to enable frequentist interpretation of convergence of posterior distributions…
Consider the problem of binary hypothesis testing. Given $Z$ coming from either $\mathbb P^{\otimes m}$ or $\mathbb Q^{\otimes m}$, to decide between the two with small probability of error it is sufficient, and in many cases necessary, to…
Bayesian inference --- although becoming popular in physics and chemistry --- is hampered up to now by the vagueness of its notion of prior probability. Some of its supporters argue that this vagueness is the unavoidable consequence of the…
In this work, we develop an objective Bayesian framework for the Dhillon probability distribution. We explicitly derive three objective priors: the Jeffreys prior, the overall reference prior, and the maximal data information prior. We show…
In Bayesian statistics the precise point-null hypothesis $\theta=\theta_0$ can be tested by checking whether $\theta_0$ is contained in a credible set. This permits testing of $\theta=\theta_0$ without having to put prior probabilities on…
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…
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…
With the advent of so-called default Bayesian hypothesis tests, scientists in applied fields have gained access to a powerful and principled method for testing hypotheses. However, such default tests usually come with a compromise,…
In this article, we propose a new method for the fundamental task of testing for dependence between two groups of variables. The response densities under the null hypothesis of independence and the alternative hypothesis of dependence are…
Bivariate count data arise in several different disciplines (epidemiology, marketing, sports statistics, etc., to name but a few) and the bivariate Poisson distribution which is a generalization of the Poisson distribution plays an…
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…
The Bayesian nonparametric inference and Dirichlet process are popular tools in statistical methodologies. In this paper, we employ the Dirichlet process in hypothesis testing to propose a Bayesian nonparametric chi-squared goodness-of-fit…
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,…
We show that the Bayesian star paradox, first proved mathematically by Steel and Matsen for a specific class of prior distributions, occurs in a wider context including less regular, possibly discontinuous, prior distributions.
An informative sampling design leads to the selection of units whose inclusion probabilities are correlated with the response variable of interest. Model inference performed on the resulting observed sample will be biased for the population…
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,…
Using instruments comprising ordered responses to items are ubiquitous for studying many constructs of interest. However, using such an item response format may lead to items with response categories infrequently endorsed or unendorsed…