Related papers: The E-measure
Backtesting risk measures is a central task in financial regulation. While standard backtests evaluate whether a forecasting model is statistically consistent with observed losses, regulatory practice often requires assessing the…
Hypothesis tests and confidence intervals are ubiquitous in empirical research, yet their connection to subsequent decision-making is often unclear. We develop a theory of certified decisions that pairs recommended decisions with…
Quantum measurements are crucial for quantum technologies and give rise to some of the most classically counter-intuitive quantum phenomena. As such, the ability to certify the presence of genuinely non-classical joint measurements in a…
There is a useful counterpart of conformal prediction for e-values, called conformal e-prediction. Conformal prediction can serve as basis for testing the assumption of exchangeability, leading to conformal testing. Similarly, conformal…
Compared to p-values, e-values provably guarantee safe, valid inference. If the goal is to test multiple hypotheses simultaneously, one can construct e-values for each individual test and then use the recently developed e-BH procedure to…
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…
Ratios of universal enumerable semimeasures corresponding to hypotheses are investigated as a solution for statistical composite hypotheses testing if an unbounded amount of computation time can be assumed. Influence testing for discrete…
We develop e-values and e-processes testing the null hypothesis that a distribution over nonnegative integers is monotone, and that a distribution over integers is unimodal given a certain mode. Our e-processes lead to tests of power one…
The measurement postulate of quantum theory stands in conflict with the laws of thermodynamics and has evoked debate regarding what actually constitutes a measurement. With the help of modern quantum statistical mechanics, we take the first…
Information theory is built on probability measures and by definition a probability measure has total mass 1. Probability measures are used to model uncertainty, and one may ask how important it is that the total mass is one. We claim that…
Change of measure inequalities translate divergences between probability measures into explicit bounds on event probabilities, and play an important role in deriving probabilistic guarantees in learning theory, information theory, and…
Proper quantification of predictive uncertainty is essential for the use of machine learning in safety-critical applications. Various uncertainty measures have been proposed for this purpose, typically claiming superiority over other…
We address the problem of uncertainty quantification and propose measures of total, aleatoric, and epistemic uncertainty based on a known decomposition of (strictly) proper scoring rules, a specific type of loss function, into a divergence…
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…
Policy learning is an important component of many real-world learning systems. A major challenge in policy learning is how to adapt efficiently to unseen environments or tasks. Recently, it has been suggested to exploit invariant…
E-values have recently emerged as a robust and flexible alternative to p-values for hypothesis testing, especially under optional continuation, i.e., when additional data from further experiments are collected. In this work, we define…
While decision theory provides an appealing normative framework for representing rich preference structures, eliciting utility or value functions typically incurs a large cost. For many applications involving interactive systems this…
The p-values are often implicitly used as a measure of evidence for the hypotheses of the tests. This practice has been analyzed with different approaches. It is generally accepted for the one-sided hypothesis problem, but it is often…
Information accounting provides a better foundation for hypothesis testing than does uncertainty quantification. A quantitative account of science is derived under this perspective that alleviates the need for epistemic bridge principles,…
We propose a new measure of deviations from expected utility theory. For any positive number~$e$, we give a characterization of the datasets with a rationalization that is within~$e$ (in beliefs, utility, or perceived prices) of expected…