Related papers: P-value: A Bless or A Curse for Evidence-Based Stu…
A nonnegative martingale with initial value equal to one measures evidence against a probabilistic hypothesis. The inverse of its value at some stopping time can be interpreted as a Bayes factor. If we exaggerate the evidence by considering…
In Bayesian statistics, the marginal likelihood, also known as the evidence, is used to evaluate model fit as it quantifies the joint probability of the data under the prior. In contrast, non-Bayesian models are typically compared using…
We introduce a joint posterior $p$-value, an extension of the posterior predictive $p$-value for multiple test statistics, designed to address limitations of existing Bayesian $p$-values in the setting of continuous model expansion. In…
Our interest is whether two binomial parameters differ, which parameter is larger, and by how much. This apparently simple problem was addressed by Fisher in the 1930's, and has been the subject of many review papers since then. Yet there…
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…
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…
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…
Genetic investigations often involve the testing of vast numbers of related hypotheses simultaneously. To control the overall error rate, a substantial penalty is required, making it difficult to detect signals of moderate strength. To…
The controversy about statistical significance vs. scientific relevance is more than 100 years old. But still nowadays null hypothesis significance testing is considered as gold standard in many empirical fields from economics and social…
While P-values are widely abused, they are a useful tool for many purposes; banning them is analogous to banning scalpels because most people do not know how to perform surgery. Many reported P-values are not genuine P-values, for a variety…
A new computation method of frequentist $p$-values and Bayesian posterior probabilities based on the bootstrap probability is discussed for the multivariate normal model with unknown expectation parameter vector. The null hypothesis is…
Hypothesis testing is a central statistical method in psychological research and the cognitive sciences. While the problems of null hypothesis significance testing (NHST) have been debated widely, few attractive alternatives exist. In this…
Mathematics is a limited component of solutions to real-world problems, as it expresses only what is expected to be true if all our assumptions are correct, including implicit assumptions that are omnipresent and often incorrect.…
Selective inference is a subfield of statistics that enables valid inference after selection of a data-dependent question. In this paper, we introduce selectively dominant p-values, a class of p-values that allow practitioners to easily…
We study a statistical framework for replicability based on a recently proposed quantitative measure of replication success, the sceptical $p$-value. A recalibration is proposed to obtain exact overall Type-I error control if the effect is…
What are the criteria that a measure of statistical evidence should satisfy? It is argued that a measure of evidence should be consistent. Consistency is an asymptotic criterion: the probability that if a measure of evidence in data…
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…
In many hypothesis testing applications, we have mixed priors, with well-motivated informative priors for some parameters but not for others. The Bayesian methodology uses the Bayes factor and is helpful for the informative priors, as it…
The following proposition is justified from several different points of view. If you use P = 0.05 to suggest that you have made a discovery, you will be wrong at least 30 percent of the time. If, as is often the case, experiments are…
Null Hypothesis Statistical Testing is a dominant framework for conducting statistical analysis across the sciences. There remains considerable debate as to whether, and under what circumstances, evidence can be said to be confirmatory of a…