Related papers: Reversibility Checking for Markov Chains
Despite its prevalence, probabilistic bisimilarity suffers from a lack of robustness under minuscule perturbations of the transition probabilities. This can lead to discontinuities in the probabilistic bisimilarity distance function,…
The basic question in perturbation analysis of Markov chains is: how do small changes in the transition kernels of Markov chains translate to chains in their stationary distributions? Many papers on the subject have shown, roughly, that the…
We consider irreversible Markov chains on finite commutative rings randomly generated using both addition and multiplication. We restrict ourselves to the case where the addition is uniformly random and multiplication is arbitrary. We first…
We propose approaches for testing implementations of Markov Chain Monte Carlo methods as well as of general Monte Carlo methods. Based on statistical hypothesis tests, these approaches can be used in a unit testing framework to, for…
We extend elliptical slice sampling, a Markov chain transition kernel suggested in Murray, Adams and MacKay 2010, to infinite-dimensional separable Hilbert spaces and discuss its well-definedness. We point to a regularity requirement,…
The aim of this work is to give an introduction to the theoretical background and computational complexity of Markov chain Monte Carlo methods. Most of the mathematical results related to the convergence are not found in most of the…
We present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the…
We present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the…
Redundancy matrices provide insights into the load carrying behavior of statically indeterminate structures. This information can be employed for the design and analysis of structures with regard to certain objectives, for example…
In this article we consider the Markovian products of invertible (not necessarily positive) matrices chosen from a strongly irreducible, contracting, finite set of matrices. We construct Markovian transfer operators and prove the spectral…
This note studies monotone Markov chains, a subclass of Markov chains with extensive applications in operations research and economics. While the properties that ensure the global stability of these chains are well studied, their…
We review recent results on the metastable behavior of continuous-time Markov chains derived through the characterization of Markov chains as unique solutions of martingale problems.
We present a data-driven model predictive control scheme for chance-constrained Markovian switching systems with unknown switching probabilities. Using samples of the underlying Markov chain, ambiguity sets of transition probabilities are…
Given a strongly stationary Markov chain and a finite set of stopping rules, we prove the existence of a polynomial algorithm which projects the Markov chain onto a minimal Markov chain without redundant information. Markov complexity is…
Motivated by techniques developed in recent progress on lower bounds for sublinear time algorithms (Behnezhad, Roghani and Rubinstein, STOC 2023, FOCS 2023, and STOC 2024) we introduce and study a new class of randomized algorithmic…
Perturbation analysis of Markov chains provides bounds on the effect that a change in a Markov transition matrix has on the corresponding stationary distribution. This paper compares and analyzes bounds found in the literature for finite…
This paper presents a novel theoretical Monte Carlo Markov chain procedure in the framework of graphs. It specifically deals with the construction of a Markov chain whose empirical distribution converges to a given reference one. The Markov…
We study the algorithmic robustness of general finite Markov chains in terms of their stationary distributions to general, adversarial corruptions of the transition matrix. We show that for Markov chains admitting a spectral gap, variants…
This article is a tutorial on Markov chain Monte Carlo simulations and their statistical analysis. The theoretical concepts are illustrated through many numerical assignments from the author's book on the subject. Computer code (in Fortran)…
We analyze the properties of degree-preserving Markov chains based on elementary edge switchings in undirected and directed graphs. We give exact yet simple formulas for the mobility of a graph (the number of possible moves) in terms of its…