Related papers: A reckless guide to P-values: local evidence, glob…
The energy test method is a multi-dimensional test of whether two samples are consistent with arising from the same underlying population, through the calculation of a single test statistic (called the $T$-value). The method has recently…
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…
When a scientist performs an experiment they normally acquire a set of measurements and are expected to demonstrate that their results are "statistically significant" thus confirming whatever hypothesis they are testing. The main method for…
High-dimensional statistical inference with general estimating equations are challenging and remain less explored. In this paper, we study two problems in the area: confidence set estimation for multiple components of the model parameters,…
Clinical research should conform to high standards of ethical and scientific integrity, given that human lives are at stake. However, economic incentives can generate conflicts of interest for investigators, who may be inclined to withhold…
Causal discovery methods based on the PC algorithm are proven to be sound if all structural assumptions are fulfilled and all conditional independence tests are correct. This idealized setting is rarely given in real data. In this work, we…
Multiple testing of a single hypothesis and testing multiple hypotheses are usually done in terms of p-values. In this paper we replace p-values with their natural competitor, e-values, which are closely related to betting, Bayes factors,…
In the hypothesis testing framework, p-value is often computed to determine rejection of the null hypothesis or not. On the other hand, Bayesian approaches typically compute the posterior probability of the null hypothesis to evaluate its…
In an attempt to provide an answer to the increasing criticism against p-values and to bridge the gap between statistical inference and prediction modelling, we introduce the probability of improved prediction (PIP). In general, the PIP is…
The persistent issue of wrongful convictions in the United States emphasizes the need for scrutiny and improvement of the criminal justice system. While statistical methods for the evaluation of forensic evidence, including glass,…
We are concerned with testing replicability hypotheses for many endpoints simultaneously. This constitutes a multiple test problem with composite null hypotheses. Traditional $p$-values, which are computed under least favourable parameter…
This article gives a survey of the e-value, a statistical significance measure a.k.a. the evidence rendered by observational data, X, in support of a statistical hypothesis, H, or, the other way around, the epistemic value of H given X. The…
Quantifying uncertainty in detected changepoints is an important problem. However it is challenging as the naive approach would use the data twice, first to detect the changes, and then to test them. This will bias the test, and can lead to…
Most scientific disciplines use significance testing to draw conclusions about experimental or observational data. This classical approach provides a theoretical guarantee for controlling the number of false positives across a set of…
We present the fundamental ideas underlying statistical hypothesis testing using the frequentist framework. We begin with a simple example that builds up the one-sample t-test from the beginning, explaining important concepts such as the…
External validity is often questionable in empirical research, especially in randomized experiments due to the trade-off between internal validity and external validity. To quantify the robustness of external validity, one must first…
We consider the problem of uncertainty assessment for low dimensional components in high dimensional models. Specifically, we propose a decorrelated score function to handle the impact of high dimensional nuisance parameters. We consider…
Large-scale multiple testing problems require the simultaneous assessment of many p-values. This paper compares several methods to assess the evidence in multiple binomial counts of p-values: the maximum of the binomial counts after…
Statistical significance testing is widely accepted as a means to assess how well a difference in effectiveness reflects an actual difference between systems, as opposed to random noise because of the selection of topics. According to…
We introduce a multiscale test statistic based on local order statistics and spacings that provides simultaneous confidence statements for the existence and location of local increases and decreases of a density or a failure rate. The…