Related papers: The e-value: A Fully Bayesian Significance Measure…
Bayesian statistics is an integral part of contemporary applied science. bayesics provides a single framework, unified in syntax and output, for performing the most commonly used statistical procedures, ranging from one- and two-sample…
The aim of this article is to make a contribution to the Bayesian procedure of testing precise hypotheses for parametric models. For this purpose, we define the Bayesian Discrepancy Measure that allows one to evaluate the suitability of a…
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…
Since its introduction by Fisher, the method of hypothesis testing that relies on computing error probabilities has witnessed several developments. Perhaps the most significant development was the seminal contributions of Neyman and Pearson…
Statistical inference has undergone a profound transformation over the past decade, evolving from a significance-testing paradigm toward a comprehensive, transparency-driven framework embedded within the broader open science ecosystem.…
A lot of Machine Learning (ML) and Deep Learning (DL) research is of an empirical nature. Nevertheless, statistical significance testing (SST) is still not widely used. This endangers true progress, as seeming improvements over a baseline…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…
Bayesian statistics is based on the subjective definition of probability as {\it ``degree of belief''} and on Bayes' theorem, the basic tool for assigning probabilities to hypotheses combining {\it a priori} judgements and experimental…
The exponential random graph (ERGM) model is a commonly used statistical framework for studying the determinants of tie formations from social network data. To test scientific theories under the ERGM framework, statistical inferential…
We discuss systematically two versions of confidence regions: those based on p-values and those based on e-values, a recent alternative to p-values. Both versions can be applied to multiple hypothesis testing, and in this paper we are…
We derive inferential procedures for large sample sizes that remain valid under data-dependent significance levels (so-called "post-hoc valid inference"). Classical statistical tools require that the significance level -- the "type-I error"…
Particle physics experiments such as those run in the Large Hadron Collider result in huge quantities of data, which are boiled down to a few numbers from which it is hoped that a signal will be detected. We discuss a simple probability…
To perform statistical inference for time series, one should be able to assess if they present deterministic or stochastic trends. For univariate analysis one way to detect stochastic trends is to test if the series has unit roots, and for…
Bayesian inference affords scientists with powerful tools for testing hypotheses. One of these tools is the Bayes factor, which indexes the extent to which support for one hypothesis over another is updated after seeing the data. Part of…
Bayes factors represent the ratio of probabilities assigned to data by competing scientific hypotheses. Drawbacks of Bayes factors are their dependence on prior specifications that define null and alternative hypotheses and difficulties…
Despite their importance in supporting experimental conclusions, standard statistical tests are often inadequate for research areas, like the life sciences, where the typical sample size is small and the test assumptions difficult to…
Classical statistical methods have theoretical justification when the sample size is predetermined. In applications, however, it's often the case that sample sizes are data-dependent rather than predetermined. The aforementioned methods…
The e-value is swiftly rising in prominence in many applications of hypothesis testing and multiple testing, yet its relationship to classical testing theory remains elusive. We unify e-values and classical testing into a single 'continuous…
This paper seeks to provide a thorough account of the ubiquitous nature of the Bayesian paradigm in modern statistics, data science and artificial intelligence. Once maligned, on the one hand by those who philosophically hated the very idea…
We study how to combine p-values and e-values, and design multiple testing procedures where both p-values and e-values are available for every hypothesis. Our results provide a new perspective on multiple testing with data-driven weights:…