Related papers: A simple two-sample Bayesian t-test for hypothesis…
Multiple testing of a single hypothesis and testing multiple hypotheses are usually done in terms of p-values. In this paper we replace p-values with their natural competitor, e-values, which are closely related to betting, Bayes factors,…
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…
In recent years, Bayesian nonparametric statistics has gathered extraordinary attention. Nonetheless, a relatively little amount of work has been expended on Bayesian nonparametric hypothesis testing. In this paper, a novel Bayesian…
Many scientifically well-motivated statistical models in natural, engineering and environmental sciences are specified through a generative process, but in some cases it may not be possible to write down a likelihood for these models…
Bayesian design of experiments and sample size calculations usually rely on complex Monte Carlo simulations in practice. Obtaining bounds on Bayesian notions of the false-positive rate and power therefore often lack closed-form or…
Statistical dependence between hypotheses poses a significant challenge to the stability of large scale multiple hypotheses testing. Ignoring it often results in an unacceptably large spread in the false positive proportion even though the…
Bayesian methods are useful for statistical inference. However, real-world problems can be challenging using Bayesian methods when the data analyst has only limited prior knowledge. In this paper we consider a class of problems, called…
This paper explores Bayesian estimation for categorical data, focusing on simple yet effective models that provide a foundation for applying more advanced methods accurately and reliably in real-world applications. We begin by revisiting…
Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature,…
This paper proposes a computationally efficient Bayesian factor model for multiple grouped count data. Adopting the link function approach, the proposed model can capture the association within and between the at-risk probabilities and…
We discuss a general approach to handling "multiple hypotheses" testing in the case when a particular hypothesis states that the vector of parameters identifying the distribution of observations belongs to a convex compact set associated…
A test based on tapering is proposed for use in testing a global linear hypothesis under a functional linear model. The test statistic is constructed as a weighted sum of squared linear combinations of Fourier coefficients, a tapered…
Cluster analysis is a fundamental research issue in statistics and machine learning. In many modern clustering methods, we need to determine whether two subsets of samples come from the same cluster. Since these subsets are usually…
The use of quadratic forms of the empirical process for the two-sample problem in the context of functional data is considered. The convergence of the family of statistics proposed to a Gaussian limit is established under metric entropy…
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…
Some scientific research questions ask to guide decisions and others do not. By their nature frequentist hypothesis-tests yield a dichotomous test decision as result, rendering them rather inappropriate for latter types of research…
Two-sample tests for multivariate data and non-Euclidean data are widely used in many fields. Parametric tests are mostly restrained to certain types of data that meets the assumptions of the parametric models. In this paper, we study a…
This introduction to Bayesian statistics presents the main concepts as well as the principal reasons advocated in favour of a Bayesian modelling. We cover the various approaches to prior determination as well as the basis asymptotic…
In an empirical Bayesian setting, we provide a new multiple testing method, useful when an additional covariate is available, that influences the probability of each null hypothesis being true. We measure the posterior significance of each…
Bayes factors are characterized by both the powerful mathematical framework of Bayesian statistics and the useful interpretation as evidence quantification. Former requires a parameter distribution that changes by seeing the data, latter…