Related papers: Hypothesis testing with e-values
Sensitivity Analysis is a framework to assess how conclusions drawn from missing outcome data may be vulnerable to departures from untestable underlying assumptions. We extend the E-value, a popular metric for quantifying robustness of…
Suppose you are told that taking a statin will reduce your risk of a heart attack or stroke by 3% in the next ten years, or that women have better emotional intelligence than men. You may wonder how accurate the 3% is, or how confident we…
There are many different notions of optimality even in testing a single hypothesis. In the multiple testing area, the number of possibilities is very much greater. The paper first will describe multiplicity issues that arise in tests…
This paper introduces a novel multi-stage decision-making model that integrates hypothesis testing and dynamic programming algorithms to address complex decision-making scenarios.Initially,we develop a sampling inspection scheme that…
Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review paper we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start…
In the footsteps of the book \textit{Measure Theory and Integration By and For the Learner} of our series in Probability Theory and Statistics, we intended to devote a special volume of the very probabilistic aspects of the first cited…
P-values are a mainstay in statistics but are often misinterpreted. We propose a new interpretation of p-value as a meaningful plausibility, where this is to be interpreted formally within the inferential model framework. We show that, for…
Conventional multiple hypothesis tests use step-up, step-down, or closed testing methods to control the overall error rates. We will discuss marrying these methods with adaptive multistage sampling rules and stopping rules to perform…
Replicability is central to scientific progress, and the partial conjunction (PC) hypothesis testing framework provides an objective tool to quantify it across disciplines. Existing PC methods assume independent studies. Yet many modern…
In this thesis I present a short review of ideas in quantum information theory. The first chapter contains introductory material, sketching the central ideas of probability and information theory. Quantum mechanics is presented at the level…
Data analysis requires translating higher level questions and hypotheses into computable statistical models. We present a mixed-methods study aimed at identifying the steps, considerations, and challenges involved in operationalizing…
We introduce a testing-by-betting framework that leverages predictions on unlabeled data to enhance the power of sequential hypothesis testing. Given limited samples from the joint distribution of $(X,Y)$, and additional unlabeled samples…
Machine learning (ML) has become a commodity in our every-day lives. We routinely ask ML empowered smartphones to suggest lovely food places or to guide us through a strange place. ML methods have also become standard tools in many fields…
Large computer-understandable proofs consist of millions of intermediate logical steps. The vast majority of such steps originate from manually selected and manually guided heuristics applied to intermediate goals. So far, machine learning…
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…
This article extends the hypotheses assessment method to the case with two competing simple hypotheses. In doing so we further clarify the benefits that hypotheses assessments can bring to classical statistical analyses. Given that…
Empirical research in Natural Language Processing (NLP) has adopted a narrow set of principles for assessing hypotheses, relying mainly on p-value computation, which suffers from several known issues. While alternative proposals have been…
This volume is a collection of six papers on the use of auxiliary information and 'a priori' values in construction of improved estimators. The work included here will be of immense application for researchers and students who emply…
Agentic AI systems execute a sequence of actions, such as reasoning steps or tool calls, in response to a user prompt. To evaluate the success of their trajectories, researchers have developed verifiers, such as LLM judges and…
This is a preliminary version of the Chapter 1 of a book "Computable Integrability"