Related papers: Two-sample Bayesian Nonparametric Hypothesis Testi…
Hypothesis testing is an essential statistical method in psychology and the cognitive sciences. The problems of traditional null hypothesis significance testing (NHST) have been discussed widely, and among the proposed solutions to the…
We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…
A Bayesian inference method for problems with small samples and sparse data is presented in this paper. A general type of prior ($\propto 1/\sigma^{q}$) is proposed to formulate the Bayesian posterior for inference problems under small…
Graph-based tests are a class of non-parametric two-sample tests useful for analyzing high-dimensional data. The test statistics are constructed from similarity graphs (such as K-minimum spanning tree), and consequently, their performance…
We consider the problem of hypothesis testing in the situation when the first hypothesis is simple and the second one is local one-sided composite. We describe the choice of the thresholds and the power functions of the Score Function test,…
Hypothesis testing is a central statistical method in psychology and the cognitive sciences. However, the problems of null hypothesis significance testing (NHST) and p-values have been debated widely, but few attractive alternatives exist.…
In this paper we study the asymptotic properties of Bayesian multiple testing procedures for a large class of Gaussian scale mixture pri- ors. We study two types of multiple testing risks: a Bayesian risk proposed in Bogdan et al. (2011)…
Instrumental variable methods allow for inference about the treatment effect by controlling for unmeasured confounding in randomized experiments with noncompliance. However, many studies do not consider the observed compliance behavior in…
In this paper we propose a new test of heteroscedasticity for parametric regression models and partial linear regression models in high dimensional settings. When the dimension of covariates is large, existing tests of heteroscedasticity…
Given two independent samples of non-negative random variables with unknown distribution functions $F$ and $G$, respectively, we introduce and discuss two tests for the hypothesis that $F$ is less than or equal to $G$ in increasing convex…
This paper presents a Bayesian framework for assessing the adequacy of a model without the necessity of explicitly enumerating a specific alternate model. A test statistic is developed for tracking the performance of the model across…
Like mean, quantile and variance, mode is also an important measure of central tendency and data summary. Many practical questions often focus on "Which element (gene or file or signal) occurs most often or is the most typical among all…
We study asymptotic properties of Bayesian multiple testing procedures and provide sufficient conditions for strong consistency under general dependence structure. We also consider a novel Bayesian multiple testing procedure and associated…
The two-sample hypothesis testing problem is studied for the challenging scenario of high dimensional data sets with small sample sizes. We show that the two-sample hypothesis testing problem can be posed as a one-class set classification…
Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well-suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing…
The following zero-sum game between nature and a statistician blends Bayesian methods with frequentist methods such as p-values and confidence intervals. Nature chooses a posterior distribution consistent with a set of possible priors. At…
We study the problem of two-sample comparison with categorical data when the contingency table is sparsely populated. In modern applications, the number of categories is often comparable to the sample size, causing existing methods to have…
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…
Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or…
In this paper we review recently developed methods for nonparametric Bayesian inference for one-dimensional diffusion models. We discuss different possible prior distributions, computational issues, and asymptotic results.