Visualizations for assessing convergence and mixing of Markov chain Monte Carlo simulations

Visualizations for Assessing Convergence and Mixing of MCMC

Bayesian inference often requires approximating the posterior distribution with Markov Chain Monte Carlo (MCMC) sampling. A central problem with MCMC is how to detect whether the simulation has converged. The samples come from the true posterior distribution only after convergence. A common solution is to start several simulations from different starting points, and measure overlap of the diffe...

Markov Chain Monte Carlo and Related Topics

This article provides a brief review of recent developments in Markov chain Monte Carlo methodology. The methods discussed include the standard Metropolis-Hastings algorithm, the Gibbs sampler, and various special cases of interest to practitioners. It also devotes a section on strategies for improving mixing rate of MCMC samplers, e.g., simulated tempering, parallel tempering, parameter expans...

izations for Assessing Convergence and Mixing of MCMC , in

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...

A Stochastic algorithm to solve multiple dimensional Fredholm integral equations of the second kind

In the present work‎, ‎a new stochastic algorithm is proposed to solve multiple dimensional Fredholm integral equations of the second kind‎. ‎The solution of the‎ integral equation is described by the Neumann series expansion‎. ‎Each term of this expansion can be considered as an expectation which is approximated by a continuous Markov chain Monte Carlo method‎. ‎An algorithm is proposed to sim...