Related papers: Compressed Hypothesis Testing: to Mix or Not to Mi…
Combining p-values from independent statistical tests is a popular approach to meta-analysis, particularly when the data underlying the tests are either no longer available or are difficult to combine. A diverse range of p-value combination…
We consider the problems of compressed sensing and optimal denoising for signals $\mathbf{x_0}\in\mathbb{R}^N$ that are monotone, i.e., $\mathbf{x_0}(i+1) \geq \mathbf{x_0}(i)$, and sparsely varying, i.e., $\mathbf{x_0}(i+1) >…
We investigate the issue of parameter estimation with nonuniform negative sampling for imbalanced data. We first prove that, with imbalanced data, the available information about unknown parameters is only tied to the relatively small…
A fast Bayesian method that seamlessly fuses classification and hypothesis testing via discriminant analysis is developed. Building upon the original discriminant analysis classifier, modelling components are added to identify…
Hypothesis testing is a key part of empirical science and multiple testing as well as the combination of evidence from several tests are continued areas of research. In this article we consider the problem of combining the results of…
We study a large-scale one-sided multiple testing problem in which test statistics follow normal distributions with unit variance, and the goal is to identify signals with positive mean effects. A conventional approach is to compute…
The problem of multiple hypothesis testing arises when there are more than one hypothesis to be tested simultaneously for statistical significance. This is a very common situation in many data mining applications. For instance, assessing…
The sequential multiple testing problem is considered under two generalized error metrics. Under the first one, the probability of at least $k$ mistakes, of any kind, is controlled. Under the second, the probabilities of at least $k_1$…
Current statistical inference problems in areas like astronomy, genomics, and marketing routinely involve the simultaneous testing of thousands -- even millions -- of null hypotheses. For high-dimensional multivariate distributions, these…
In this paper, we develop a general approach for probabilistic estimation and optimization. An explicit formula and a computational approach are established for controlling the reliability of probabilistic estimation based on a mixed…
We introduce a new statistical test based on the observed spacings of ordered data. The statistic is sensitive to detect non-uniformity in random samples, or short-lived features in event time series. Under some conditions, this new test…
A hypothesis testing scheme for entanglement has been formulated based on the Poisson distribution framework instead of the POVM framework. Three designs were proposed to test the entangled states in this framework. The designs were…
It is generally believed that more observations provide more information. However, we observe that in the independence test for rare events, the power of the test is, surprisingly, determined by the number of rare events rather than the…
Hypothesis testing results often rely on simple, yet important assumptions about the behaviour of the distribution of p-values under the null and the alternative. We examine tests for one dimensional parameters of interest that converge to…
In this paper, an alternative mixed Poisson distribution is proposed by amalgamating Poisson distribution and a modification of the Quasi Lindley distribution. Some fundamental structural properties of the new distribution, namely the shape…
Symmetry plays a central role in the sciences, machine learning, and statistics. For situations in which data are known to obey a symmetry, a multitude of methods that exploit symmetry have been developed. Statistical tests for the presence…
In this paper, we study the problem of testing whether or not a given probability measure $\mu$ on $\mathbb{R}^{d}$ can be decomposed as a mixture of two probability measures whose second order statistics are significantly different. We…
We propose an approach to rapidly find the upper limit of separability between datasets that is directly applicable to HEP classification problems. The most common HEP classification task is to use $n$ values (variables) for an object…
A nonparametric anomalous hypothesis testing problem is investigated, in which there are totally n sequences with s anomalous sequences to be detected. Each typical sequence contains m independent and identically distributed (i.i.d.)…
We study the problem of testing, using only a single sample, between mean field distributions (like Curie-Weiss, Erd\H{o}s-R\'enyi) and structured Gibbs distributions (like Ising model on sparse graphs and Exponential Random Graphs). Our…