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We develop exact Markov chain Monte Carlo methods for discretely-sampled, directly and indirectly observed diffusions. The qualification "exact" refers to the fact that the invariant and limiting dist...
We present a framework for obtaining explicit bounds on the rate of convergence to equilibrium of a Markov chain on a general state space, with respect to both total variation and Wasserstein distance...
A general purpose variance reduction technique for Markov chain Monte Carlo estimators based on the zero-variance principle introduced in the physics literature by Assaraf and Caffarel (1999, 2003), i...
In this paper, we introduce the notion of efficiency (consistency) and examine some asymptotic properties of Markov chain Monte Carlo methods. We apply these results to the Gibbs sampler for independe...
The correspondence between the cross-entropymethod and the zero-variance approximation to simulate a rare event problem in Markov chains is shown. This leads to a sufficient condition that the cross...
The reversible jump Markov chain Monte Carlo sampler (Green, 1995) provides a general framework for Markov chain Monte Carlo (MCMC) simulation in which the dimension of the parameter space can vary ...
In Bayesian inference, the posterior distribution for parameters  2  is given by (jy) / (yj)(), where one's prior beliefs about the unknown parameters, as expressed through the prior distrib...
In this note we attempt to trace the history and development of Markov chain Monte Carlo (MCMC) from its early inception in the late 1940’s through its use today. We see how the earlier stages of th...
In this paper,we combine useful aspects of both approaches.On the one hand,we are inspired by the discretization, where filtering for the state process is possible,on the other hand,we catch attracti...
Hidden Markov models (HMMs) and related models have become stan- dard in statistics during the last 15C2 years, with applications in diverse areas like speech and other statistical signal processing...
In this paper, we study the following model of hidden Markov chain: $Y_i=X_i+varepsilon_i$, $ i=1,dots,n+1$ with $(X_i)$ a real-valued stationary Markov chain and $(varepsilon_i)_{1leq ileq n+1}$ a no...
The goal of this expository paper is to describe conditions which guarantee a central limit theorem for functionals of general state space Markov chains. This is done with a view towards Markov chain ...
Markov chain comparison     Markov chains  mixing time  comparison       2009/5/18
This is an expository paper, focussing on the following scenario. We have two Markov chains, M and M'. By some means, we have obtained a bound on the mixing time of M'. We wish to compare M with M' in...
Given a probability law $pi$ on a set S and a function $g : S rightarrow R$, suppose one wants to estimate the mean $bar{g} = int g dpi$. The Markov Chain Monte Carlo method consists of inventing and ...

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