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Statistical inference may follow a frequentist approach or it may follow a Bayesian approach or it may use the minimum description length principle (MDL). Our goal is to identify situations in which these different approaches to statistical…
One of the crucial differences between mathematical models of classical and quantum mechanics is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an…
Canonical variables for the Poisson algebra of quantum moments are introduced here, expressing semiclassical quantum mechanics as a canonical dynamical system that extends the classical phase space. New realizations for up to fourth order…
A sequence of random variables is exchangeable if its joint distribution is invariant under variable permutations. We introduce exchangeable variable models (EVMs) as a novel class of probabilistic models whose basic building blocks are…
Generation of deviates from random graph models with non-trivial edge dependence is an increasingly important problem. Here, we introduce a method which allows perfect sampling from random graph models in exponential family form…
We present an abstract framework for asymptotic analysis of convergence based on the notions of eventual families of sets that we define. A family of subsets of a given set is called here an "eventual family" if it is upper hereditary with…
In their fundamental paper on cubic variance functions, Letac and Mora (The Annals of Statistics,1990) presented a systematic, rigorous and comprehensive study of natural exponential families on the real line, their characterization through…
Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…
We describe the notion of a quantum family of maps of a quantum space and that of a quantum commutant of such a family. Quantum commutants are quantum semigroups defined by a certain universal property. We give a few examples of these…
Starting from the basic-exponential, a q-deformed version of the exponential function established in the framework of the basic-hypergeometric series, we present a possible formulation of a generalized statistical mechanics. In a…
An understanding of quantum theory in terms of new, underlying descriptions capable of explaining the existence of non-classical correlations, non-commutativity of measurements and other unique and counter-intuitive phenomena remains still…
The closure of a discrete exponential family is described by a finite set of equations corresponding to the circuits of an underlying oriented matroid. These equations are similar to the equations used in algebraic statistics, although they…
In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg…
The exploration of complex physical or technological processes usually requires exploiting available information from different sources: (i) physical laws often represented as a family of parameter dependent partial differential equations…
We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…
Despite the flexibility and popularity of mixture models, their associated parameter spaces are often difficult to represent due to fundamental identification problems. This paper looks at a novel way of representing such a space for…
It is possible to completely explain all aspects of quantum mechanics by expressing the relations between physical properties in terms of complex conditional probabilities (Phys. Rev. A 89, 042115(2014)). These fully deterministic…
A new family of polynomials, called cumulant polynomial sequence, and its extensions to the multivariate case is introduced relied on a purely symbolic combinatorial method. The coefficients of these polynomials are cumulants, but depending…
Recently, it has been argued that no extension of quantum theory can have improved predictive power under a strong assumption of free choice of the experimental settings and validity of quantum mechanics. Here, under a different free choice…
We celebrate this year hundred years of quantum mechanics but there is still no consensus regarding its interpretation and limitations. In this article we advocate the statistical contextual interpretation which is free of paradoxes. State…