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When observations are organized into groups where commonalties exist amongst them, the dependent random measures can be an ideal choice for modeling. One of the propositions of the dependent random measures is that the atoms of the…
Partially exchangeable sequences representable as mixtures of Markov chains are completely specified by de Finetti's mixing measure. The paper characterizes, in terms of a subclass of hidden Markov models, the partially exchangeable…
Conformal prediction is a popular, modern technique for providing valid predictive inference for arbitrary machine learning models. Its validity relies on the assumptions of exchangeability of the data, and symmetry of the given model…
We propose an elementary but effective approach to studying a general class of Poissonized tenable and balanced urns on two colors. We characterize the asymptotic behavior of the process via a partial differential equation that governs the…
We consider a version of the classical P\'olya urn scheme which incorporates innovations. The space $S$ of colors is an arbitrary measurable set. After each sampling of a ball in the urn, one returns $C$ balls of the same color and…
A classical problem in statistics is estimating the expected coverage of a sample, which has had applications in gene expression, microbial ecology, optimization, and even numismatics. Here we consider a related extension of this problem to…
Exchangeability is a central notion in statistics and probability theory. The assumption that an infinite sequence of data points is exchangeable is at the core of Bayesian statistics. However, finite exchangeability as a statistical…
We define a simple rule that allows to describe sequences of projective measurements for a broad class of generalized probabilistic models. This class embraces quantum mechanics and classical probability theory, but, for example, also the…
The probabilities of causation are commonly used to solve decision-making problems. Tian and Pearl derived sharp bounds for the probability of necessity and sufficiency (PNS), the probability of sufficiency (PS), and the probability of…
Recent research has established sufficient conditions for finite mixture models to be identifiable from grouped observations. These conditions allow the mixture components to be nonparametric and have substantial (or even total) overlap.…
McKean-Vlasov stochastic differential equations (MV-SDEs) provide a mathematical description of the behavior of an infinite number of interacting particles by imposing a dependence on the particle density. As such, we study the influence of…
We explore the relationship between possibility measures (supremum preserving normed measures) and p-boxes (pairs of cumulative distribution functions) on totally preordered spaces, extending earlier work in this direction by De Cooman and…
We propose a way of finding a Stein type characterization of a given absolutely continuous distribution $\mu$ on $\R$ which is motivated by a regression property satisfied by an exchangeable pair $(W,W')$ where $\calL(W)$ is supposed or…
Permutation tests are a powerful and flexible approach to inference via resampling. As computational methods become more ubiquitous in the statistics curriculum, use of permutation tests has become more tractable. At the heart of the…
Collective behaviors that emerge from interactions are fundamental to numerous biological systems. To learn such interacting forces from observations, we introduce a measure-valued neural network that infers measure-dependent interaction…
Conditional identity in distribution (Berti et al. (2004)) is a new type of dependence for random variables, which generalizes the well-known notion of exchangeability. In this paper, a class of random sequences, called Generalized Species…
The experimentally measured multiplicity distributions exhibit, after closer inspection, peculiarly enhanced void probability and oscillatory behavior of the modified combinants. We show that both these features can be used as additional…
We argue for the use of separate exchangeability as a modeling principle in Bayesian nonparametric (BNP) inference. Separate exchangeability is de facto widely applied in the Bayesian parametric case, e.g., it naturally arises in simple…
Conformal inference is a fundamental and versatile tool that provides distribution-free guarantees for many machine learning tasks. We consider the transductive setting, where decisions are made on a test sample of $m$ new points, giving…
Finite mixture models are statistical models which appear in many problems in statistics and machine learning. In such models it is assumed that data are drawn from random probability measures, called mixture components, which are…