Related papers: Accurate $p$-Value Calculation for Generalized Fis…

Permutation tests are widely used for statistical hypothesis testing when the sampling distribution of the test statistic under the null hypothesis is analytically intractable or unreliable due to finite sample sizes. One critical challenge…

$\textbf{Motivation:}$ Small $p$-values are often required to be accurately estimated in large-scale genomic studies for the adjustment of multiple hypothesis tests and the ranking of genomic features based on their statistical…

We introduce a method for computation of exact conditional efficiency robust enumeration p-values for detection of genotype--phenotype associations at a single bi-allelic genetic locus. Our method can be based on any arbitrary ranking test…

The topic of multiple hypotheses testing now has a potpourri of novel theories and ubiquitous applications in diverse scientific fields. However, the universal utility of this field often hinders the possibility of having a generalized…

Existing methods for high-dimensional changepoint detection and localization typically focus on changes in either the mean vector or the covariance matrix separately. This separation reduces detection power and localization accuracy when…

Bayesian inference can often be sensitive to the choice of hyperparameters of the prior or likelihood, yet defining and quantifying this sensitivity in a principled and computationally feasible way remains challenging in practice.…

We introduce a method for calculating \(p\)-values to test causal hypotheses in qualitative research \emph{a la} process tracing. As in an experiment, our \(p\)-value tells us how often one would make the same or more compelling…

Various methods of combining individual p-values into one p-value are widely used in many areas of statistical applications. We say that a combining method is valid for arbitrary dependence (VAD) if it does not require any assumption on the…

Generalized partially linear single-index additive models (GPLSIAMs) have been increasingly applied across diverse areas due to their versatility in integrating functional flexibility with parametric dimension reduction while maintaining…

We establish a precise connection between statistical significance in dependence testing and information-theoretic dependence as quantified by Shannon mutual information (MI). In the absence of prior distributional information, we consider…

Significance testing based on p-values has been implicated in the reproducibility crisis in scientific research, with one of the proposals being to eliminate them in favor of Bayesian analyses. Defenders of the p-values have countered that…

As the amount and complexity of available data increases, the need for robust statistical learning becomes more pressing. To enhance resilience against model misspecification, the generalized posterior inference method adjusts the…

Gaussian mixture models (GMMs) are fundamental tools in statistical and data sciences. We study the moments of multivariate Gaussians and GMMs. The $d$-th moment of an $n$-dimensional random variable is a symmetric $d$-way tensor of size…

The notion of p-value is a fundamental concept in statistical inference and has been widely used for reporting outcomes of hypothesis tests. However, p-value is often misinterpreted, misused or miscommunicated in practice. Part of the issue…

Permutation tests are amongst the most commonly used statistical tools in modern genomic research, a process by which p-values are attached to a test statistic by randomly permuting the sample or gene labels. Yet permutation p-values…

The problem of testing the equality of mean vectors for high-dimensional data has been intensively investigated in the literature. However, most of the existing tests impose strong assumptions on the underlying group covariance matrices…

Detecting dependence between two random variables is a fundamental problem. Although the Pearson correlation is effective for capturing linear dependency, it can be entirely powerless for detecting nonlinear and/or heteroscedastic patterns.…

Pearson's correlation is among the mostly widely reported measures of association. The strength of the statistical evidence for linear association is determined by the p-value of a hypothesis test. If the true distribution of a dataset is…

Machine learning techniques typically rely on large datasets to create accurate classifiers. However, there are situations when data is scarce and expensive to acquire. This is the case of studies that rely on state-of-the-art computational…

This paper develops a multifidelity method that enables estimation of failure probabilities for expensive-to-evaluate models via information fusion and importance sampling. The presented general fusion method combines multiple probability…