Related papers: Evidential Analysis: An Alternative to Hypothesis …
Statistical hypothesis testing is the central method to demarcate scientific theories in both exploratory and inferential analyses. However, whether this method befits such purpose remains a matter of debate. Established approaches to…
One can argue that one of the main roles of the subject of statistics is to characterize what the evidence in collected data says about questions of scientific interest. There are two broad questions that we will refer to as the estimation…
Hypothesis testing and model choice are quintessential questions for statistical inference and while the Bayesian paradigm seems ideally suited for answering these questions, it faces difficulties of its own ranging from prior modelling to…
A number of biomedical problems require performing many hypothesis tests, with an attendant need to apply stringent thresholds. Often the data take the form of a series of predictor vectors, each of which must be compared with a single…
Statistical hypotheses are translations of scientific hypotheses into statements about one or more distributions, often concerning their centre. Tests that assess statistical hypotheses of centre implicitly assume a specific centre, e.g.,…
Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…
Testing of hypotheses is a well studied topic in mathematical statistics. Recently, this issue has also been addressed in the context of Inverse Problems, where the quantity of interest is not directly accessible but only after the…
Statistical analysis is an important tool to distinguish systematic from chance findings. Current statistical analyses rely on distributional assumptions reflecting the structure of some underlying model, which if not met lead to problems…
A two-sample hypothesis test is a statistical procedure used to determine whether the distributions generating two samples are identical. We consider the two-sample testing problem in a new scenario where the sample measurements (or sample…
The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…
We introduce credal two-sample testing, a new hypothesis testing framework for comparing credal sets -- convex sets of probability measures where each element captures aleatoric uncertainty and the set itself represents epistemic…
The fundamental elements of evidential reasoning problems are described, followed by a discussion of the structure of various types of problems. Bayesian inference networks and state space formalism are used as the tool for problem…
Much of science is (rightly or wrongly) driven by hypothesis testing. Even in situations where the hypothesis testing paradigm is correct, the common practice of basing inferences solely on p-values has been under intense criticism for over…
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…
Evidential deep learning, built upon belief theory and subjective logic, offers a principled and computationally efficient way to turn a deterministic neural network uncertainty-aware. The resultant evidential models can quantify…
Trustworthy ML systems should not only return accurate predictions, but also a reliable representation of their uncertainty. Bayesian methods are commonly used to quantify both aleatoric and epistemic uncertainty, but alternative…
In science and medicine, model interpretations may be reported as discoveries of natural phenomena or used to guide patient treatments. In such high-stakes tasks, false discoveries may lead investigators astray. These applications would…
Testing hypotheses is an issue of primary importance in the scientific research, as well as in many other human activities. Much clarification about it can be achieved if the process of learning from data is framed in a stochastic model of…
Evidential reasoning is cast as the problem of simplifying the evidence-hypothesis relation and constructing combination formulas that possess certain testable properties. Important classes of evidence as identifiers, annihilators, and…
The asymptotically optimal hypothesis testing problem with the general sources as the null and alternative hypotheses is studied under exponential-type error constraints on the first kind of error probability. Our fundamental philosophy in…