Related papers: The E-measure
A standard practice in statistical hypothesis testing is to mention the p-value alongside the accept/reject decision. We show the advantages of mentioning an e-value instead. With p-values, it is not clear how to use an extreme observation…
E-variables are nonnegative random variables with expected value at most one under any distribution from a given null hypothesis. Every nonasymptotically valid test can be obtained by thresholding some e-variable. As such, e-variables arise…
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…
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,…
Quality statistical inference requires a sufficient amount of data, which can be missing or hard to obtain. To this end, prediction-powered inference has risen as a promising methodology, but existing approaches are largely limited to…
A recurring debate in the philosophy of statistics concerns what, exactly, should count as a measure of evidence for or against a given hypothesis. P-values, likelihood ratios, and Bayes factors all have their defenders. In this paper we…
In contemporary research, data scientists often test an infinite sequence of hypotheses $H_1,H_2,\ldots$ one by one, and are required to make real-time decisions without knowing the future hypotheses or data. In this paper, we consider such…
Conformal prediction is a powerful framework for distribution-free uncertainty quantification. The standard approach to conformal prediction relies on comparing the ranks of prediction scores: under exchangeability, the rank of a future…
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 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:…
Plausibility measures are structures for reasoning in the face of uncertainty that generalize probabilities, unifying them with weaker structures like possibility measures and comparative probability relations. So far, the theory of…
Given information about which options a decision-maker definitely rejects from given finite sets of options, we study the implications for decision-making with E-admissibility. This means that from any finite set of options, we reject those…
E-variables are a relatively new approach for testing statistical hypotheses that has been experiencing major development during the last several years. In this paper we introduce the method of e-variable-approximability and use it to…
We develop a representation of a decision maker's uncertainty based on e-variables. Like the Bayesian posterior, this *e-posterior* allows for making predictions against arbitrary loss functions that may not be specified ex ante. Unlike the…
We examine a new approach to modeling uncertainty based on plausibility measures, where a plausibility measure just associates with an event its plausibility, an element is some partially ordered set. This approach is easily seen to…
If uncertainty is modelled by a probability measure, decisions are typically made by choosing the option with the highest expected utility. If an imprecise probability model is used instead, this decision rule can be generalised in several…
In the context of supervised parametric models, we introduce the concept of e-values. An e-value is a scalar quantity that represents the proximity of the sampling distribution of parameter estimates in a model trained on a subset of…
Hypothesis testing via e-variables can be framed as a sequential betting game, where a player each round picks an e-variable. A good player's strategy results in an effective statistical test that rejects the null hypothesis as soon as…
Complex high-dimensional co-occurrence data are increasingly popular from a complex system of interacting physical, biological and social processes in discretely indexed modifiable areal units or continuously indexed locations of a study…
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…