Related papers: Continuity of the Mixing Operator
Clustering is the process of finding underlying group structures in data. Although mixture model-based clustering is firmly established in the multivariate case, there is a relative paucity of work on matrix variate distributions and none…
Multimodal normal incestual systems are investigated in terms of multiple categories. The different sorted composition of operators are exhibited as 2-cells in multiple categories built up from 2-categories giving rise to different axioms.…
In this article, we introduce mixture representations for likelihood ratio ordered distributions. Essentially, the ratio of two probability densities, or mass functions, is monotone if and only if one can be expressed as a mixture of…
We consider a model of coupled oscillators which can be seen as a gain and loss system. In the attempt to quantize the system we propose a new definition of multiplication between distributions, and we check that this definition can be…
We consider the notion of the matrix (tensor) distribution of a measurable function of several variables. On the one hand, it is an invariant of this function with respect to a certain group of transformations of variables; on the other…
This paper presents an in-depth analysis of a parametrized version of the resolvent composition, an operation that combines a set-valued operator and a linear operator. We provide new properties and examples, and show that resolvent…
Quantum mechanics predicts the joint probability distributions of the outcomes of simultaneous measurements of commuting observables, but the current formulation lacks the operational definition of simultaneous measurements. In order to…
Measurements are shown to be processes designed to return figures: they are effective. This effectivity allows for a formalization as Turing machines, which can be described employing computation theory. Inspired in the halting problem we…
Finite mixture distributions arise in sampling a heterogeneous population. Data drawn from such a population will exhibit extra variability relative to any single subpopulation. Statistical models based on finite mixtures can assist in the…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
This paper is the first part of a project devoted to studying the interconnection between controllability properties of a dynamical system and the large-time asymptotics of trajectories for the associated stochastic system. It is proved…
The primary purpose of this paper is to investigate the question of invertibility of the sum of operators. The setting is bounded and unbounded linear operators. Some interesting examples and consequences are given. As an illustrative…
Considerable interest has recently been focused on studying multiple phenotypes simultaneously in both epidemiological and genomic studies, either to capture the multidimensionality of complex disorders or to understand shared etiology of…
A simply structured distributed observer is described for estimating the state of a continuous-time, jointly observable, input-free, linear system whose sensed outputs are distributed across a time-varying network. It is explained how to…
We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error…
We develop elements of a general dilation theory for operator-valued measures and bounded linear maps between operator algebras that are not necessarily completely-bounded. We prove our main results by extending and generalizing some known…
Over the past decades, linear mixed models have attracted considerable attention in various fields of applied statistics. They are popular whenever clustered, hierarchical or longitudinal data are investigated. Nonetheless, statistical…
Many interesting families of polynomials are indexed by permutations or related objects, and are defined by applying divided difference operators, modified by polynomials, on some initial base case. The fact that these constructions produce…
A solution is given to the basic distributed feedback control problem for a multi-channel linear system assuming only that the system is jointly controllable, jointly observable and has an associated neighbor graph which is strongly…
An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture…