Related papers: Countable Partially Exchangeable Mixtures
This note attempts to understand graph limits as defined by Lovasz and Szegedy (2006)} in terms of harmonic analysis on semigroups. This is done by representing probability distributions of random exchangeable graphs as mixtures of…
Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k$-th order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both…
The paper considers a stochastic differential equation of Duffing type with Markov coefficients. The existence of unpredictable solutions is considered. The unpredictability is a property of bounded functions characterized by unbounded…
Mixture models are a fundamental tool in applied statistics and machine learning for treating data taken from multiple subpopulations. The current practice for estimating the parameters of such models relies on local search heuristics…
For a class of piecewise deterministic Markov processes, the supports of the invariant measures are characterized. This is based on the analysis of controllability properties of an associated deterministic control system. Its invariant…
It is shown that the combinatorics of commutation relations is well suited for analyzing the convergence rate of certain Markov chains. Examples studied include random walk on irreducible representations, a local random walk on partitions…
We study a strengthening of the notion of a perfectly meager set. We say that that a subset $A$ of a perfect Polish space $X$ is countably perfectly meager in $X$, if for every sequence of perfect subsets $\{P_n: n \in {\mathbb N}\}$ of…
The aim of this paper is to prove an improved version of the bounded differences inequality for matrix valued functions, by developing the methods of Mackey et al.: "Matrix Concentration Inequalities via the Method of Exchangeable Pairs".…
We give a de Finetti type representation for exchangeable random coalescent trees (formally described as semi-ultrametrics) in terms of sampling iid sequences from marked metric measure spaces. We apply this representation to define…
We show that if the density of the absolutely continuous part of a copula is bounded away from zero on a set of Lebesgue measure 1, then that copula generates \textquotedblleft lower $\psi$-mixing\textquotedblright\ stationary Markov…
The collective interference of partially distinguishable bosons in multi-mode networks is studied via double-sided Feynman diagrams. The probability for many-body scattering events becomes a multi-dimensional tensor-permanent, which…
A random vector $X=(X_1,\ldots,X_n)$ with the $X_i$ taking values in an arbitrary measurable space $(S, \mathscr{S})$ is exchangeable if its law is the same as that of $(X_{\sigma(1)}, \ldots, X_{\sigma(n)})$ for any permutation $\sigma$.…
A simple Markov process is considered involving a diffusion in one direction and a transport in a transverse direction. Quantitative mixing rate estimates are obtained with limited assumptions about the transport field, which might be…
Based on previous work of Paul Ressel and myself, I show that the space of all "continuous" exchangeable probability measures on a certain set of order processes is a Bauer simplex.
Given a finite admixture model whose components and weights are unknown, let the number of identifiable components be a function of the amount of data sampled from a known distribution on the unit simplex. We use techniques from stochastic…
We discuss the efficient computation of performance, reliability, and availability measures for Markov chains; these metrics, and the ones obtained by combining them, are often called performability measures. We show that this computational…
In this paper, we prove that finite state space non parametric hidden Markov models are identifiable as soon as the transition matrix of the latent Markov chain has full rank and the emission probability distributions are linearly…
We prove a conjecture of Diaconis and Freedman (Ann. Probab. 1980) characterising the extreme points of the set of partially-exchangeable processes on a countable set. More concretely, we prove that the partially exchangeable sigma-algebra…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
General Markov chains with a countably additive transition probability in arbitrary phase space are considered. Markov operators extend from the space of countably additive measures to the space of finitely additive measures. In the…