But how do we actually construct a Markov chain with a stationary distribution equal to our target distribution? Also, we want this method to have a good (that is, small) mixing time. The Metropolis method allows us achieve these goals by defining our Markov chain as a random walk over a suitably defined graph. We define the approach as follows. Say we which to sample values i ∈ Ω from a distri...

This study considers using Metropolis-Hastings algorithm for stochastic simulation of chemical reactions. The proposed method uses SSA (Stochastic Simulation Algorithm) distribution which is a standard method for solving well-stirred chemically reacting systems as a desired distribution. A new numerical solvers based on exponential form of exact and approximate solutions of CME (Chemical Master...

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We describe a Metropolis-Hastings algorithm for sampling formal concepts, i.e., closed (item-) sets, according to any desired strictly positive distribution. Important applications are (a) estimating the number of all formal concepts as well as (b) discovering any number of interesting, non-redundant, and representative local patterns. Setting (a) can be used for estimating the runtime of algor...

The Metropolis Light Transport algorithm is a variant of the classic Metropolis method used in statistical physics. A variance analysis of the Metropolis Light Transport algorithm is presented that bounds its variance in terms of the number of paths used and the intrinsic correlation between samples. It is shown that the variance of a pixel is where is the number of samples for the entire image...

(First draft March 2005; revised November 2005) Abstract This paper extends some adaptive schemes that have been developed for the Random Walk Metropolis algorithm to more general versions of the Metropolis-Hastings (MH) algorithm, particularly to the Metropolis Adjusted Langevin algorithm of Roberts and Tweedie (1996). Our simulations show that the adaptation drastically improves the performan...

We introduce an adaptive output-sensitive Metropolis-Hastings algorithm for probabilistic models expressed as programs, Adaptive Lightweight Metropolis-Hastings (AdLMH). The algorithm extends Lightweight Metropolis-Hastings (LMH) by adjusting the probabilities of proposing random variables for modification to improve convergence of the program output. We show that AdLMH converges to the correct...

This paper describes modeling discrete event systems in Metropolis using one of the key concepts employed by Metropolis, orthogonalization of design aspects, which in this particular case, is the orthogonalization between capability and cost. To support the orthogonalization, quantity annotation mechanism is introduced. This paper formally analyzes simulation strategies for quantity annotation ...

1 Department of Mathematics, Lorestan University, P.O. Box 465, Khoramabad, Iran 2 Department of Civil Engineering, Shahid Chamran University, P.O. Box 135, Ahvaz, Iran 3 School of Engineering and Science, Victoria University, P.O. Box 14428, Melbourne, MC 8001, Australia 4 School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, ...

We present a novel Metropolis-Hastings method for large datasets that uses small expected-size minibatches of data. Previous work on reducing the cost of MetropolisHastings tests yield variable data consumed per sample, with only constant factor reductions versus using the full dataset for each sample. Here we present a method that can be tuned to provide arbitrarily small batch sizes, by adjus...