When a graph can be decomposed into clusters of well connected subgraphs, it is possible to speed up random walks taking advantage of the topology of the graph. In this work, a new random walk scheme is introduced and a condition is given when the new random walk performs better than the Metropolis algorithm.

In this paper we address the problem of the prohibitively large computational cost of existing Markov chain Monte Carlo methods for large–scale applications with high dimensional parameter spaces, e.g. in uncertainty quantification in porous media flow. We propose a new multilevel Metropolis-Hastings algorithm, and give an abstract, problem dependent theorem on the cost of the new multilevel es...

A proper choice of a proposal distribution for Markov chain Monte Carlo methods, for example for the Metropolis±Hastings algorithm, is well known to be a crucial factor for the convergence of the algorithm. In this paper we introduce an adaptive Metropolis (AM) algorithm, where the Gaussian proposal distribution is updated along the process using the full information cumulated so far. Due to th...

A proper choice of a proposal distribution for MCMC methods, e.g. for the Metropolis-Hastings algorithm, is well known to be a crucial factor for the convergence of the algorithm. In this paper we introduce an adaptive Metropolis Algorithm (AM), where the Gaussian proposal distribution is updated along the process using the full information cumulated so far. Due to the adaptive nature of the pr...

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We propose a new Metropolis-Hastings algorithm for sampling from smooth, unimodal distributions; a restriction to the method is that the target be optimizable. The method can be viewed as a mixture of two types of MCMC algorithm; specifically, we seek to combine the versatility of the random walk Metropolis and the efficiency of the independence sampler as found with various types of target dis...