Related papers: Some things we've learned (about Markov chain Mont…
The preparation of the stationary distribution of irreducible, time-reversible Markov chains is a fundamental building block in many heuristic approaches to algorithmically hard problems. It has been conjectured that quantum analogs of…
We elaborate the idea behind Markov chain Monte Carlo (MCMC) methods in a mathematically coherent, yet simple and understandable way. To this end, we proof a pivotal convergence theorem for finite Markov chains and a minimal version of the…
Markov chain Monte Carlo methods have become popular in statistics as versatile techniques to sample from complicated probability distributions. In this work, we propose a method to parameterize and train transition kernels of Markov chains…
Markov chain Monte Carlo algorithms play a key role in the Bayesian approach to phylogenetic inference. In this paper, we present the first theoretical work analyzing the rate of convergence of several Markov chains widely used in…
Improved rates of convergence for ergodic homogeneous Markov chains are studied. In comparison to the earlier papers the setting is also generalised to the case without a unique dominated measure. Examples are provided where the new bound…
Markov chain Monte Carlo is an inherently serial algorithm. Although likelihood calculations for individual steps can sometimes be parallelized, the serial evolution of the process is widely viewed as incompatible with parallelization,…
In the paper, we study a new rate of convergence estimate for homogeneous discrete-time nonlinear Markov chains based on the Markov-Dobrushin condition. This result generalizes the convergence estimates for any positive number of transition…
This paper considers the optimal control of time varying continuous time Markov chains whose transition rates are themselves Markov processes. In one set of problems the solution of an ordinary differential equation is shown to determine…
This paper introduces a class of Monte Carlo algorithms which are based upon the simulation of a Markov process whose quasi-stationary distribution coincides with a distribution of interest. This differs fundamentally from, say, current…
Markov chains are a class of probabilistic models that have achieved widespread application in the quantitative sciences. This is in part due to their versatility, but is compounded by the ease with which they can be probed analytically.…
This note provides several recent progresses in the study of long time behavior of Markov processes. The examples presented below are related to other scientific fields as PDE's, physics or biology. The involved mathematical tools as…
We propose a new approach for estimating the finite dimensional transition matrix of a Markov chain using a large number of independent sample paths observed at random times. The sample paths may be observed as few as two times, and the…
Markov chain Monte Carlo (MCMC) algorithms provide a very general recipe for estimating properties of complicated distributions. While their use has become commonplace and there is a large literature on MCMC theory and practice, MCMC users…
Strongly Rayleigh distributions are natural generalizations of product and determinantal probability distributions and satisfy strongest form of negative dependence properties. We show that the "natural" Monte Carlo Markov Chain (MCMC) is…
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)…
The problem of estimating an unknown discrete distribution from its samples is a fundamental tenet of statistical learning. Over the past decade, it attracted significant research effort and has been solved for a variety of divergence…
The problem of detecting a sinusoidal signal with randomly varying frequency has a long history. It is one of the core problems in signal processing, arising in many applications including, for example, underwater acoustic frequency line…
Lecture notes (in French) of a master 2 level course in applied mathematics. Contents: Part I. Markov chains on a countable space. 1. Examples 2. Summary of basic properties. 3. Spectral theory and speed of convergence. 4. Lyapunov…
Sequential Monte Carlo Samplers are a class of stochastic algorithms for Monte Carlo integral estimation w.r.t. probability distributions, which combine elements of Markov chain Monte Carlo methods and importance sampling/resampling…
A powerful tool for studying long-term convergence of a Markov process to its stationary distribution is a Lyapunov function. In some sense, this is a substitute for eigenfunctions. For a stochastically ordered Markov process on the…