Markov Chain Monte Carlo Algorithms: Theory and Practice
نویسنده
چکیده
We describe the importance and widespread use of Markov chain Monte Carlo (MCMC) algorithms, with an emphasis on the roles in which theoretical analysis can help with their practical implementation. In particular, we discuss how to achieve rigorous quantitative bounds on convergence to stationarity using the coupling method together with drift and minorisation conditions. We also discuss recent advances in the field of adaptive MCMC, where the computer iteratively selects from among many different MCMC algorithms. Such adaptive MCMC algorithms may fail to converge if implemented naively, but they will converge correctly if certain conditions such as Diminishing Adaptation are satisfied.
منابع مشابه
Markov Chain Monte Carlo Methods : Computation and Inference
This chapter reviews the recent developments in Markov chain Monte Carlo simulation methods These methods, which are concerned with the simulation of high dimensional probability distributions, have gained enormous prominence and revolutionized Bayesian statistics The chapter provides background on the relevant Markov chain theory and provides detailed information on the theory and practice of ...
متن کاملSpatial count models on the number of unhealthy days in Tehran
Spatial count data is usually found in most sciences such as environmental science, meteorology, geology and medicine. Spatial generalized linear models based on poisson (poisson-lognormal spatial model) and binomial (binomial-logitnormal spatial model) distributions are often used to analyze discrete count data in which spatial correlation is observed. The likelihood function of these models i...
متن کاملThe random walk Metropolis: linking theory and practice through a case study
The random walk Metropolis: linking theory and practice through a case study. Summary: The random walk Metropolis (RWM) is one of the most common Markov Chain Monte Carlo algorithms in practical use today. Its theoretical properties have been extensively explored for certain classes of target, and a number of results with important practical implications have been derived. This article draws to...
متن کاملOn automating Markov chain Monte Carlo for a class of spatial models
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 still have to contend with several challenges with each implementation of the algorithm. These challenges include determining how to construct an efficient a...
متن کامل