Related papers: Element-Free Probability Distributions and Random …
Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases…
In this paper, we consider nonparametric multidimensional finite mixture models and we are interested in the semiparametric estimation of the population weights. Here, the i.i.d. observations are assumed to have at least three components…
A main task in data analysis is to organize data points into coherent groups or clusters. The stochastic block model is a probabilistic model for the cluster structure. This model prescribes different probabilities for the presence of edges…
A distribution of electromagnetic fields presents a statistical assembly of a particular type, which is at scale h a quantum statistical assembly itself and has also been instrumental to concretisation of the basic probability assumption of…
Bayesian probability theory is used to analyze the oft-made assumption that humans are typical observers in the universe. Some theoretical calculations make the {\it selection fallacy} that we are randomly chosen from a class of objects by…
Compression of integer sets and sequences has been extensively studied for settings where elements follow a uniform probability distribution. In addition, methods exist that exploit clustering of elements in order to achieve higher…
Quasi-set theory provides us a mathematical background for dealing with collections of indistinguishable elementary particles. In this paper, we show how to obtain the usual statistics (Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac)…
The need to condition distributional properties such as expectation, variance, and entropy arises in algorithmic fairness, model simplification, robustness and many other areas. At face value however, distributional properties are not…
There is a growing interest in the so-called Bayesian Predictive Inference approach, which allows to perform Bayesian inference without specifying the likelihood and prior of the model, or the need of any MCMC. Instead, only a sequence of…
This paper studies the role played by identification in the Bayesian analysis of statistical and econometric models. First, for unidentified models we demonstrate that there are situations where the introduction of a non-degenerate prior…
We want to select the best systems out of a given set of systems (or rank them) with respect to their expected performance. The systems allow random observations only and we assume that the joint observation of the systems has a…
The Bayesian approach to machine learning amounts to computing posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables.…
Random matrix theory (RMT) is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors presented…
We introduce a general Bayesian framework for graph matching grounded in a new theory of exchangeable random permutations. Leveraging the cycle representation of permutations and the literature on exchangeable random partitions, we define,…
We are concerned in clustering continuous data sets subject to non-ignorable missingness. We perform clustering with a specific semi-parametric mixture, under the assumption of conditional independence given the component. The mixture model…
We introduce semiparametric Bayesian networks that combine parametric and nonparametric conditional probability distributions. Their aim is to incorporate the advantages of both components: the bounded complexity of parametric models and…
With the rapid expansion of graphs and networks and the growing magnitude of data from all areas of science, effective treatment and compression schemes of context-dependent data is extremely desirable. A particularly interesting direction…
\noindent In our contribution to this volume we deal with \emph{discrete} symmetries: these are symmetries based upon groups with a discrete set of elements (generally a set of elements that can be enumerated by the positive integers). In…
Expressions for the entropy and equations for the quantum distribution functions in systems of non-interacting fermions and bosons with an arbitrary, including small, number of particles are obtained in the paper
The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…