Related papers: A synthetic approach to Markov kernels, conditiona…

The paper studies an improved estimate for the rate of convergence for nonlinear homogeneous discrete-time Markov chains. These processes are nonlinear in terms of the distribution law. Hence, the transition kernels are dependent on the…

We consider a discrete latent variable model for two-way data arrays, which allows one to simultaneously produce clusters along one of the data dimensions (e.g. exchangeable observational units or features) and contiguous groups, or…

Possibilistic conditional independence is investigated: we propose a definition of this notion similar to the one used in probability theory. The links between independence and non-interactivity are investigated, and properties of these…

We review a recent development at the interface between discrete mathematics on one hand and probability theory and statistics on the other, specifically the use of Markov chains and their boundary theory in connection with the asymptotics…

Imprecise probability is concerned with uncertainty about which probability distributions to use. It has applications in robust statistics and machine learning. We look at programming language models for imprecise probability. Our…

This paper introduces a decision-theoretic framework for constructing and evaluating test statistics based on their relationship with ancillary statistics-quantities whose distributions remain fixed under the null and alternative…

We consider a type of Markov property for set-indexed processes which is satisfied by all processes with independent increments and which allows us to introduce a transition system theory leading to the construction of the process. A…

A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the…

As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using It\^o's formula and on a new…

A novel strategy that combines a given collection of $\pi$-reversible Markov kernels is proposed. At each Markov transition, one of the available kernels is selected via a state-dependent probability distribution. In contrast to random-scan…

Multi-state models are frequently applied for representing processes evolving through a discrete set of state. Important classes of multi-state models arise when transitions between states may depend on the time since entry into the current…

In this paper we develop a general framework for constructing and analysing coupled Markov chain Monte Carlo samplers, allowing for both (possibly degenerate) diffusion and piecewise deterministic Markov processes. For many performance…

For Markov processes with absorption, we provide general criteria ensuring the existence and the exponential non-uniform convergence in total variation norm to a quasi-stationary distribution. We also characterize a subset of its domain 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…

We generalize Franz' independence in tensor categories with inclusions from two morphisms (which represent generalized random variables) to arbitrary ordered families of morphisms. We will see that this only works consistently if the unit…

Hypothesis tests are a crucial statistical tool for data mining and are the workhorse of scientific research in many fields. Here we study differentially private tests of independence between a categorical and a continuous variable. We take…

We consider a family of Markov chains whose transition dynamics are affected by model parameters. Understanding the parametric dependence of (complex) performance measures of such Markov chains is often of significant interest. The…

In this note, we consider general growth-fragmentation equations from a probabilistic point of view. Using Foster-Lyapunov techniques, we study the recurrence of the associated Markov process depending on the growth and fragmentation rates.…

We present a novel method for computing reachability probabilities of parametric discrete-time Markov chains whose transition probabilities are fractions of polynomials over a set of parameters. Our algorithm is based on two key…

In this work we take a Category Theoretic perspective on the relationship between probabilistic modeling and function approximation. We begin by defining two extensions of function composition to stochastic process subordination: one based…