相关论文: On the Existence of Uniformly Most Powerful Bayesi…
Uniformly most powerful tests are statistical hypothesis tests that provide the greatest power against a fixed null hypothesis among all tests of a given size. In this article, the notion of uniformly most powerful tests is extended to the…
The recently introduced framework of universal inference provides a new approach to constructing hypothesis tests and confidence regions that are valid in finite samples and do not rely on any specific regularity assumptions on the…
In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the…
Model selection for Gaussian concentration graph is based on multiple testing of pairwise conditional independence. In practical applications partial correlation tests are widely used. However it is not known whether partial correlation…
We address the following question in this paper: "What are the most robust statistical methods for social choice?'' By leveraging the theory of uniformly least favorable distributions in the Neyman-Pearson framework to finite models and…
The small sample universal hypothesis testing problem is investigated in this paper, in which the number of samples $n$ is smaller than the number of possible outcomes $m$. The goal of this work is to find an appropriate criterion to…
The classical likelihood ratio test (LRT) based on the asymptotic chi-squared distribution of the log likelihood is one of the fundamental tools of statistical inference. A recent universal LRT approach based on sample splitting provides…
This paper introduces a feasible and practical Bayesian method for unit root testing in financial time series. We propose a convenient approximation of the Bayes factor in terms of the Bayesian Information Criterion as a straightforward and…
Generalizations to the permutation test are introduced to allow for situations in which the null model is not exchangeable. It is shown that the generalized permutation tests are exact, and a partial converse: that any test function that is…
We derive uniformly most powerful (UMP) tests for simple and one-sided hypotheses for a population proportion within the framework of Differential Privacy (DP), optimizing finite sample performance. We show that in general, DP hypothesis…
This paper is concerned with a Bayesian approach to testing hypotheses in statistical inverse problems. Based on the posterior distribution $\Pi \left(\cdot |Y = y\right)$, we want to infer whether a feature $\langle\varphi,…
We present the $U$-Statistic Permutation (USP) test of independence in the context of discrete data displayed in a contingency table. Either Pearson's chi-squared test of independence, or the $G$-test, are typically used for this task, but…
Like all sub-fields of machine learning Bayesian Deep Learning is driven by empirical validation of its theoretical proposals. Given the many aspects of an experiment it is always possible that minor or even major experimental flaws can…
In this paper, we propose novel, fully Bayesian non-parametric tests for one-sample and two-sample multivariate location problems. We model the underlying distribution using a Dirichlet process prior, and develop a testing procedure based…
This paper concerns the construction of tests for universal hypothesis testing problems, in which the alternate hypothesis is poorly modeled and the observation space is large. The mismatched universal test is a feature-based technique for…
In the multiple regression model we prove that the coefficient t-test for a variable of interest is uniformly most powerful unbiased, with the other parameters considered nuisance. The proof is based on the theory of tests with…
We extend a recently proposed 1-nearest-neighbor based multiclass learning algorithm and prove that our modification is universally strongly Bayes-consistent in all metric spaces admitting any such learner, making it an "optimistically…
We investigate a generalized empirical likelihood approach in a two-group setting where the constraints on parameters have a form of U-statistics. In this situation, the summands that consist of the constraints for the empirical likelihood…
The structural characterization of high-dimensional mutually unbiased bases (MUBs) by classifying MUBs subsets remains a major open problem. The existing methods not only fail to conclude on the exact classification, but also are severely…
We introduce a rigorous and sensitive significance test for hyperuniformity that yields reliable results even from a single sample. Our approach is based on a detailed analysis of the empirical Fourier transform of a stationary point…