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We present new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. Our theory builds on the idea of using subsets of the full data to establish consistency of estimators based on the full…
The quasiprobability representation of quantum states addresses two main concerns, the identification of nonclassical features and the decomposition of the density operator. While the former aspect is a main focus of current research, the…
We discuss the (re-)construction of quasiprobability representations from generic measurements, including noisy ones. Based on the measurement under study, quasiprobabilities and the associated concept of nonclassicality are introduced. A…
Modeling of high order multivariate probability distribution is a difficult problem which occurs in many fields. Copula approach is a good choice for this purpose, but the curse of dimensionality still remains a problem. In this paper we…
Conformal prediction is widely used to equip black-box machine learning models with uncertainty quantification, offering formal coverage guarantees under exchangeable data. However, these guarantees fail when faced with subpopulation…
We consider the set of the power non-negative polynomials of several variables and its subset that consists of polynomials which can be represented as a sum of squares. It is shown in the classic work by D.Hilbert that it is a proper…
Quasi-probabilities appear across diverse areas of physics, but their conceptual foundations remain unclear: they are often treated merely as computational tools, and operations like conditioning and Bayes' theorem become ambiguous. We…
A flexible representation of uncertainty that remains within the standard framework of probabilistic measure theory is presented along with a study of its properties. This representation relies on a specific type of outer measure that is…
In this work, the concept of mutually unbiased frames is introduced as the most general notion of unbiasedness for sets composed by linearly independent and normalized vectors. It encompasses the already existing notions of unbiasedness for…
The synthesis of robust invariant sets for nonlinear systems has traditionally been hindered by the inherent non convexity and a strict reliance on exact analytical models. This paper presents a purely data-driven framework to compute…
Let $N$ be a simply connected, connected non-commutative nilpotent Lie group with Lie algebra $\mathfrak{n}$ having rational structure constants. We assume that $N=P\rtimes M,$ $M$ is commutative, and for all $\lambda\in…
The article is devoted to the study of exponential statistical structures of type B, which constitute a subclass of exponential families of probability distributions. This class is characterized by a number of analytical and probabilistic…
A collapse-free version of quantum theory is examined to systematically study the role of the projection postulate. This foil theory assumes "passive" measurements that do not update quantum states although measurement outcomes still occur…
The framework of non-extensive statistical mechanics, proposed by Tsallis, has been used to describe a variety of systems. The non-extensive statistical mechanics is usually introduced in a formal way, thus simple models exhibiting some…
We examine the effectiveness of assuming an equal probability for states far from equilibrium. For this aim, we propose a method to construct a master equation for extensive variables describing non-stationary nonequilibrium dynamics. The…
A flexible semiparametric class of models is introduced that offers an alternative to classical regression models for count data as the Poisson and negative binomial model, as well as to more general models accounting for excess zeros that…
Patterns on numerical semigroups are multivariate linear polynomials, and they are said to be admissible if there exists a numerical semigroup such that evaluated at any nonincreasing sequence of elements of the semigroup gives integers…
With respect to earlier investigations, the theory of multi-component, concentric, copolar, axisymmetric, rigidly rotating polytropes is improved and extended, including subsystems with nonzero density on the boundary and subsystems with…
The Contextuality-by-Default approach to determining and measuring the (non)contextuality of a system of random variables requires that every random variable in the system be represented by an equivalent set of dichotomous random variables.…
We investigate the supports of extremal martingale measures with pre-specified marginals in a two-period setting. First, we establish in full generality the equivalence between the extremality of a given measure $Q$ and the denseness in…