Related papers: Empirical partially Bayes two sample testing
We consider the problem of testing means from samples of two populations for which the labels are not defined with certainty. We show that this problem is connected to another one that is testing expected values of components of…
This paper develops new insights into quantitative methods for the validation of computational model prediction. Four types of methods are investigated, namely classical and Bayesian hypothesis testing, a reliability-based method, and an…
A common problem in genetics is that of testing whether a set of highly dependent gene expressions differ between two populations, typically in a high-dimensional setting where the data dimension is larger than the sample size. Most…
The null hypothesis test (NHT) is widely used for validating scientific hypotheses but is actually highly criticized. Although Bayesian tests overcome several criticisms, some limits remain. We propose a Bayesian two-interval test (2IT) in…
Permutation testing in linear models, where the number of nuisance coefficients is smaller than the sample size, is a well-studied topic. The common approach of such tests is to permute residuals after regressing on the nuisance covariates.…
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…
This paper develops Bayesian sample size formulae for experiments comparing two groups. We assume the experimental data will be analysed in the Bayesian framework, where pre-experimental information from multiple sources can be represented…
We propose a fast and theoretically grounded method for Bayesian variable selection and model averaging in latent variable regression models. Our framework addresses three interrelated challenges: (i) intractable marginal likelihoods, (ii)…
The Behrens-Fisher Problem is a classical statistical problem. It is to test the equality of the means of two normal populations using two independent samples, when the equality of the population variances is unknown. Linnik (1968) has…
The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…
We propose a new empirical Bayes approach for inference in the $p \gg n$ normal linear model. The novelty is the use of data in the prior in two ways, for centering and regularization. Under suitable sparsity assumptions, we establish a…
Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…
In this article the issues are discussed with the Bayesian approach, least-square fits, and most-likely fits. Trying to counter these issues, a method, based on weighted confidence, is proposed for estimating probabilities and other…
Many testing problems are readily amenable to randomised tests such as those employing data splitting. However despite their usefulness in principle, randomised tests have obvious drawbacks. Firstly, two analyses of the same dataset may…
We consider the problem of integrating a small probability sample (ps) and a non-probability sample (nps). By definition, for the nps, there are no survey weights, but for the ps, there are survey weights. The key issue is that the nps,…
In practical situations, most experimental designs often yield unbalanced data which have different numbers of observations per unit because of cost constraints, or missing data, etc. In this paper, we consider the Bayesian approach to…
Estimation of the allele frequency at genetic markers is a key ingredient in biological and biomedical research, such as studies of human genetic variation or of the genetic etiology of heritable traits. As genetic data becomes increasingly…
We develop a method to perform model averaging in two-stage linear regression systems subject to endogeneity. Our method extends an existing Gibbs sampler for instrumental variables to incorporate a component of model uncertainty. Direct…
We revisit the problem of simultaneously testing the means of $n$ independent normal observations under sparsity. We take a Bayesian approach to this problem by introducing a scale-mixture prior known as the normal-beta prime (NBP) prior.…
We consider a Bayesian framework for estimating the sample size of a clinical trial. The new approach, called BESS, is built upon three pillars: Sample size of the trial, Evidence from the observed data, and Confidence of the final decision…