Markov chain Monte Carlo (MCMC) algorithms are used to estimate features of interest of a distribution. The Monte Carlo error in estimation has an asymptotic normal distribution whose multivariate nature has so far been ignored in the MCMC community. We present a class of multivariate spectral variance estimators for the asymptotic covariance matrix in the Markov chain central limit theorem and...

Monte Carlo (MC) sampling methods are widely applied in Bayesian inference, system simulation and optimization problems. The Markov Chain Monte Carlo (MCMC) algorithms are a well-known class of MC methods which generate a Markov chain with the desired invariant distribution. In this document, we focus on the Metropolis-Hastings (MH) sampler, which can be considered as the atom of the MCMC techn...

In this paper, the Markov chain Monte Carlo (MCMC) method has been used to estimate the parameters of Exponentiated Gumbel(EG) model based on a complete sample. A procedure is developed to obtain Bayes estimates of the parameters of the Exponentiated Gumbel model using MCMC simulation method in OpenBUGS, an established software for Bayesian analysis using Markov Chain Monte Carlo (MCMC) method....

RÉSUMÉ. Les méthodes de Monte Carlo par chaînes de Markov (MCMC) couplées à des modèles de Markov cachés sont utilisées dans de nombreux domaines, notamment en environnement et en écologie. Sur des exemples simples, nous montrons que la vitesse de convergence de ces méthodes peut être très faible. Nous proposons de mettre en interaction plusieurs algorithmes MCMC pour accélérer cette convergenc...

We present a Markov chain Monte Carlo (MCMC) method for generating Markov chains using Markov bases for conditional independence models for a fourway contingency table. We then describe a Markov basis characterized by Markov properties associated with a given conditional independence model and show how to use the Markov basis to generate random tables of a Markov chain. The estimates of exact p...

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 schemes. We develop a stability analysis by functional inequalities for a nonlinear flow of probability measures describing the limit behavior of the algorithms as ...

This paper investigates the potential of a cellular automata (CA) model based on logistic regression (logit) and Markov Chain Monte Carlo (MCMC) to simulate the dynamics of urban growth. The model assesses urbanization likelihood based on (i) a set of urban development driving forces (calibrated based on logit) and (ii) the land-use of neighboring cells (calibrated based on MCMC). An innovative...

Multicanonical MCMC (Multicanonical Markov Chain Monte Carlo; Multicanonical Monte Carlo) is discussed as a method of rare event sampling. Starting from a review of the generic framework of importance sampling, multicanonical MCMC is introduced, followed by applications in random matrices, random graphs, and chaotic dynamical systems. Replica exchange MCMC (also known as parallel tempering or M...

Markov chain Monte Carlo (MCMC) is a popular class of algorithms to sample from a complex distribution. A key issue in the design of MCMC algorithms is to improve the proposal mechanism and the mixing behaviour. This has led some authors to propose the use of a population of MCMC chains, while others go even further by integrating techniques from evolutionary computation (EC) into the MCMC fram...

Metropolis-Hastings Markov chain Monte Carlo (MCMC) algorithms and other popular MCMC algorithms induce a Markov chain which has the target distribution as its stationary distribution. Optimal scaling refers to the need to tune the parameters of the proposal kernel in order to ensure the Markov chain obtained from the algorithm converges as fast as possible to stationarity. Theoretical results ...