Related papers: Uniformly most powerful Bayesian tests
Like all sub-fields of machine learning Bayesian Deep Learning is driven by empirical validation of its theoretical proposals. Given the many aspects of an experiment it is always possible that minor or even major experimental flaws can…
The American Statistical Association (ASA) statement on statistical significance and P-values \cite{wasserstein2016asa} cautioned statisticians against making scientific decisions solely on the basis of traditional P-values. The statement…
We derive a new class of statistical tests for generalized linear models based on thresholding point estimators. These tests can be employed whether the model includes more parameters than observations or not. For linear models, our tests…
Along the lines of Janssen's and Pfanzagl's work the testing theory for statistical functionals is further developed for non-parametric one-sample problems. Efficient tests for the one-sided and two-sided problems are derived for…
We look at the distribution of the Bayesian evidence for mock realizations of supernova and baryon acoustic oscillation data. The ratios of Bayesian evidences of different models are often used to perform model selection. The significance…
Bayesian model comparison is often based on the posterior distribution over the set of compared models. This distribution is often observed to concentrate on a single model even when other measures of model fit or forecasting ability…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions are a special case where the density matrix is restricted to be diagonal. Density…
A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining…
Testing differences in mean vectors is a fundamental task in the analysis of high-dimensional compositional data. Existing methods may suffer from low power if the underlying signal pattern is in a situation that does not favor the deployed…
The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…
Pimentel et al. (2020) recently analysed probing from an information-theoretic perspective. They argue that probing should be seen as approximating a mutual information. This led to the rather unintuitive conclusion that representations…
We develop the theory of hypothesis testing based on the e-value, a notion of evidence that, unlike the p-value, allows for effortlessly combining results from several studies in the common scenario where the decision to perform a new study…
A theory of measurement uncertainty is presented, which, since it is based exclusively on the Bayesian approach and on the subjective concept of conditional probability, is applicable in the most general cases. The recent International…
We introduce a probabilistic robustness measure for Bayesian Neural Networks (BNNs), defined as the probability that, given a test point, there exists a point within a bounded set such that the BNN prediction differs between the two. Such a…
The theory of testing statistical functionals is developed for non-parametric two-sample problems. For differentiable real-valued statistical functionals, some tests for the one-sided and two-sided cases are proposed and studied. The…
It is well known that a Bayesian probability forecast for all future observations should be a probability measure in order to satisfy a natural condition of coherence. The main topics of this paper are the evolution of the Bayesian…
Motivated by the likelihood ratio test under the Gaussian assumption, we develop a maximum sum-of-squares test for conducting hypothesis testing on high dimensional mean vector. The proposed test which incorporates the dependence among the…
Bayesian tests on the symmetry of the generalized von Mises model for planar directions (Gatto and Jammalamadaka, 2007) are introduced. The generalized von Mises distribution is a flexible model that can be axially symmetric or asymmetric,…
Theory testing in the physical sciences has been revolutionized in recent decades by Bayesian approaches to probability theory. Here, I will consider Bayesian approaches to theory extensions, that is, theories like inflation which aim to…
The Bayes factor, the data-based updating factor from prior to posterior odds, is a principled measure of relative evidence for two competing hypotheses. It is naturally suited to sequential data analysis in settings such as clinical trials…