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The use of standard statistical methods, such as maximum likelihood, is often justified based on their asymptotic properties. For suitably regular models, this theory is standard but, when the model is non-regular, e.g., the support depends…

Can a physicist make only a finite number of errors in the eternal quest to uncover the law of nature? This millennium-old philosophical problem, known as inductive inference, lies at the heart of epistemology. Despite its significance to…

An inferential model (IM) is a model describing the construction of provably reliable, data-driven uncertainty quantification and inference about relevant unknowns. IMs and Fisher's fiducial argument have similar objectives, but a…

Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…

Ideally, all analyses of normally distributed data should include the full covariance information between all data points. In practice, the full covariance matrix between all data points is not always available. Either because a result was…

Arrow's Impossibility Theorem is a seminal result of Social Choice Theory that demonstrates the impossibility of ranked-choice decision-making processes to jointly satisfy a number of intuitive and seemingly desirable constraints. The…

This article presents methods for estimating extreme probabilities, beyond the range of the observations. These methods are model-free and applicable to almost any sample size. They are grounded in order statistics theory and have a wide…

This paper considers the problem of testing whether there exists a non-negative solution to a possibly under-determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of…

Empirical science needs to be based on facts and claims that can be reproduced. This calls for replicating the studies that proclaim the claims, but practice in most fields still fails to implement this idea. When such studies emerged in…

We establish nonparametric identification in a class of so-called index models using a novel approach that relies on general topological results. Our proof strategy requires substantially weaker conditions on the functions and distributions…

We develop inference procedures robust to general forms of weak dependence. The procedures utilize test statistics constructed by resampling in a manner that does not depend on the unknown correlation structure of the data. We prove that…

One problem to solve in the context of information fusion, decision-making, and other artificial intelligence challenges is to compute justified beliefs based on evidence. In real-life examples, this evidence may be inconsistent,…

Plausibility measures are structures for reasoning in the face of uncertainty that generalize probabilities, unifying them with weaker structures like possibility measures and comparative probability relations. So far, the theory of…

Adequacy for estimation between an inferential method and a model can be de{\ldots}ned through two main requirements: {\ldots}rstly the inferential tool should de{\ldots}ne a well posed problem when applied to the model; secondly the…

We elucidate a close connection between the Theory of Judgment Aggregation (more generally, Evaluation Aggregation), and a relatively young but rapidly growing field of universal algebra, that was primarily developed to investigate…

Recovering and distinguishing between the strict-preference, indifference and/or indecisiveness parts of a decision maker's preferences is a challenging task but also important for testing theory and conducting welfare analysis. This paper…

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…

Continuing our investigation into the Hierarchical Reference Theory of fluids for thermodynamic states of infinite isothermal compressibility kappa[T] we now turn to the available numerical evidence to elucidate the character of the partial…

There are things we know, things we know we don't know, and then there are things we don't know we don't know. In this paper we address the latter two issues in a Bayesian framework, introducing the notion of doubt to quantify the degree of…

Computing the reachability probability in infinite state probabilistic models has been the topic of numerous works. Here we introduce a new property called \emph{divergence} that when satisfied allows to compute reachability probabilities…