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Universal outlier hypothesis testing refers to a hypothesis testing problem where one observes a large number of length-$n$ sequences -- the majority of which are distributed according to the typical distribution $\pi$ and a small number…
The prediction interval has been increasingly used in meta-analyses as a useful measure for assessing the magnitude of treatment effect and between-studies heterogeneity. In calculations of the prediction interval, although the…
Established frameworks to understand problems with reproducibility in science begin with the relationship between our understanding of the prior probability of a claim and the statistical certainty that should be demanded of it, and explore…
Pairwise comparison models have been widely used for utility evaluation and rank aggregation across various fields. The increasing scale of modern problems underscores the need to understand statistical inference in these models when the…
Frank Porter has recently posted a review of "Confidence intervals for the Poisson distribution" (arXiv:2509.02852). The long, diverse history of such intervals is closely related to that of confidence intervals for the parameter of the…
The Posterior distribution of the Likelihood Ratio (PLR) is proposed by Dempster in 1974 for significance testing in the simple vs composite hypotheses case. In this hypotheses test case, classical frequentist and Bayesian hypotheses tests…
The Mordell-Lang conjecture describes the intersection of a finitely generated subgroup with a closed subvariety of a semiabelian variety. Equivalently, this conjecture describes the intersection of closed subvarieties with the set of…
Simpson's Paradox is a well-known phenomenon in statistical science, where the relationship between the response variable $X$ and a certain explanatory factor of interest $A$ reverses when an additional factor $B_1$ is considered. This…
Hardy's paradox provides an all-versus-nothing fashion to directly certify that quantum mechanics cannot be completely described by local realistic theory. However, when considering potential imperfections in experiments, like imperfect…
Bayes [Philos. Trans. R. Soc. Lond. 53 (1763) 370--418; 54 296--325] introduced the observed likelihood function to statistical inference and provided a weight function to calibrate the parameter; he also introduced a confidence…
The fundamental proposal in this article is that logical formulas of the form (f <-> ~f) are not contradictions, and that formulas of the form (t <-> t) are not tautologies. Such formulas, wherever they appear in mathematics, are instead…
This paper re-examines the first normalized incomplete moment, a well-established measure of inequality with wide applications in economic and social sciences. Despite the popularity of the measure itself, existing statistical inference…
A relativistic version of the (consistent or decoherent) histories approach to quantum theory is developed on the basis of earlier work by Hartle, and used to discuss relativistic forms of the paradoxes of spherical wave packet collapse,…
The belief that numbers offer a single, objective description of reality overlooks a crucial truth: data does not speak for itself. Every dataset results from choices-what to measure, how, when, and with whom-which inevitably reflect…
Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…
Both the Kullback-Leibler and the Tsallis divergence have a strong limitation: if the value $0$ appears in probability distributions $\left( p_{1},\cdots ,p_{n}\right)$ and $\left( q_{1},\cdots ,q_{n}\right)$, it must appear in the same…
Consider the problem of high dimensional variable selection for the Gaussian linear model when the unknown error variance is also of interest. In this paper, we show that the use of conjugate shrinkage priors for Bayesian variable selection…
Philosophers now seem to agree that frequentism is an untenable strategy to explain the meaning of probabilities. Nevertheless, I want to revive frequentism, and I will do so by grounding probabilities on typicality in the same way as the…
Mixture models are one of the most widely used statistical tools when dealing with data from heterogeneous populations. This paper considers the long-standing debate over finite mixture and infinite mixtures and brings the two modelling…
We study the problem of mismatched binary hypothesis testing between i.i.d. distributions. We analyze the tradeoff between the pairwise error probability exponents when the actual distributions generating the observation are different from…