Constructing optimal transition matrix for Markov chain Monte Carlo

On the Optimal Transition Matrix for Markov Chain Monte Carlo Sampling

Constructing Optimal Transition Matrix Formarkov Chain Monte Carlo via Global Optimization

The notion of asymptotic variance has been used as a means for performance evaluation of MCMCmethods. An imperative task when constructing a Markov chain for the Monte Carlo simulation with prescribed stationary distribution is to optimize the asymptotic variance. Cast against an appropriately chosen coordinate system, the worst-case analysis of the asymptotic variance arising in MCMC can be fo...

Markov Chain Monte Carlo

Markov chain Monte Carlo is an umbrella term for algorithms that use Markov chains to sample from a given probability distribution. This paper is a brief examination of Markov chain Monte Carlo and its usage. We begin by discussing Markov chains and the ergodicity, convergence, and reversibility thereof before proceeding to a short overview of Markov chain Monte Carlo and the use of mixing time...

Markov Chain Monte Carlo

This paper gives a brief introduction to Markov Chain Monte Carlo methods, which offer a general framework for calculating difficult integrals. We start with the basic theory of Markov chains and build up to a theorem that characterizes convergent chains. We then discuss the MetropolisHastings algorithm.

Markov chain Monte Carlo

One of the simplest and most powerful practical uses of the ergodic theory of Markov chains is in Markov chain Monte Carlo (MCMC). Suppose we wish to simulate from a probability density π (which will be called the target density) but that direct simulation is either impossible or practically infeasible (possibly due to the high dimensionality of π). This generic problem occurs in diverse scient...