Related papers: Total positivity in Markov structures
This paper investigates natural conditions for the existence of optimal policies for a Markov decision process with incomplete information (MDPII) and with expected total costs. The MDPII is the classic model of a controlled stochastic…
Structural independence is the (conditional) independence that arises from the structure rather than the precise numerical values of a distribution. We develop this concept and relate it to $d$-separation and structural causal models.…
In this work we establish the posterior consistency for a parametrized family of partially observed, fully dominated Markov models. As a main assumption, we suppose that the prior distribution assigns positive probability to all…
This paper presents a focused review of Markov random fields (MRFs)--commonly used probabilistic representations of spatial dependence in discrete spatial domains--for categorical data, with an emphasis on models for binary-valued…
This paper analyzes independence concepts for sets of probability measures associated with directed acyclic graphs. The paper shows that epistemic independence and the standard Markov condition violate desirable separation properties. The…
We propose a score test for dependence predictability in conditional copulas that is robust to temporal instabilities. Our semiparametric procedure accommodates flexible dynamics in the marginal processes and remains agnostic about the…
Mekler's construction gives an interpretation of any structure in a finite relational language in a group (nilpotent of class $2$ and exponent $p>2$, but not finitely generated in general). Even though this construction is not a…
We propose a family of tests of the validity of the assumptions underlying independent component analysis methods. The tests are formulated as L2-type procedures based on characteristic functions and involve weights; a proper choice of…
The variability of structure in a finite Markov equivalence class of causally sufficient models represented by directed acyclic graphs has been fully characterized. Without causal sufficiency, an infinite semi-Markov equivalence class of…
After reviewing the main properties of time-evolutions of open quantum systems, some considerations about the positivity of factorized Markovian dynamics for bipartite systems are made. In particular, it is shown that the positivity of the…
A new sufficient condition is proved for the existence of stochastic semigroups generated by the sum of two unbounded operators. It is applied to one-dimensional piecewise deterministic Markov processes, where we also discuss the existence…
We consider a Markov chain on $R^+$ with asymptotically zero drift and finite second moments of jumps which is positive recurrent. A power-like asymptotic behaviour of the invariant tail distribution is proven; such a heavy-tailed invariant…
The theory of dependency graphs is a powerful toolbox to prove asymptotic normality of sums of random variables. In this article, we introduce a more general notion of weighted dependency graphs and give normality criteria in this context.…
Selfadhesivity is a property of entropic polymatroids which guarantees that the polymatroid can be glued to an identical copy of itself along arbitrary restrictions such that the two pieces are independent given the common restriction. We…
We show that, for generative classifiers, conditional independence corresponds to linear constraints for the induced discrimination functions. Discrimination functions of undirected Markov network classifiers can thus be characterized by…
We propose a new notion of positivity for topological field theories (TFTs), based on S. Eilenberg's concept of completeness for semirings. We show that a complete ground semiring, a system of fields on manifolds and a system of action…
A graphical model encodes conditional independence relations via the Markov properties. For an undirected graph these conditional independence relations can be represented by a simple polytope known as the graph associahedron, which can be…
Suppose we are given the conditional probability of one variable given some other variables.Normally the full joint distribution over the conditioning variablesis required to determine the probability of the conditioned variable.Under what…
A covariance graph is an undirected graph associated with a multivariate probability distribution of a given random vector where each vertex represents each of the different components of the random vector and where the absence of an edge…
Statistical properties of infinite products of random isotropically distributed matrices are investigated. Both for continuous processes with finite correlation time and discrete sequences of independent matrices, a formalism that allows to…