in recent years, some statisticians have studied the signal detection problem by using the random field theory. in this paper we have considered point estimation of the gaussian scale space random field parameters in the bayesian approach. since the posterior distribution for the parameters of interest dose not have a closed form, we introduce the markov chain monte carlo (mcmc) algorithm to ap...

The covariance ordering, for discrete and continuous time Markov chains, is defined and studied. This partial ordering gives a necessary and sufficient condition for MCMC estimators to have small asymptotic variance. Connections between this ordering, eigenvalues, and suprema of the spectrum of the Markov transition kernel, are provided. A representation of the asymptotic variance of MCMC estim...

We present a Markov chain Monte Carlo (MCMC) method for generating Markov chains using Markov bases for conditional independence models for a fourway contingency table. We then describe a Markov basis characterized by Markov properties associated with a given conditional independence model and show how to use the Markov basis to generate random tables of a Markov chain. The estimates of exact p...

Subset Simulation is an adaptive simulation method that efficiently solves structural reliability problems with many random variables. The method requires sampling from conditional distributions, which is achieved through Markov Chain Monte Carlo (MCMC) algorithms. This paper discusses different MCMC algorithms proposed for Subset Simulation and introduces a novel approach for MCMC sampling in ...

This letter considers how a number of modern Markov chain Monte Carlo (MCMC) methods can be applied for parameter estimation and inference in state-space models with point process observations. We quantified the efficiencies of these MCMC methods on synthetic data, and our results suggest that the Reimannian manifold Hamiltonian Monte Carlo method offers the best performance. We further compare...

While adaptive methods for MCMC are under active development, their utility has been under-recognized. We briefly review some theoretical results relevant to adaptive MCMC. We then suggest a very simple and effective algorithm to adapt proposal densities for random walk Metropolis and Metropolis adjusted Langevin algorithms. The benefits of this algorithm are immediate, and we demonstrate its p...

In this scribe, we are going to review the Parallel Monte Carlo Markov Chain (MCMC) method. First, we will recap of MCMC methods, particularly the Metropolis-Hasting and Gibbs Sampling algorithms. Then we will show the drawbacks of these classical MCMC methods as well as the Naive Parallel Gibbs Sampling approach. Finally, we will come up with the Sequential Monte Carlo and Parallel Inference f...

This paper concerns the introduction of a new Markov Chain Monte Carlo scheme for posterior sampling in Bayesian nonparametric mixture models with priors that belong to the general Poisson-Kingman class. We present a novel compact way of representing the infinite dimensional component of the model such that while explicitly representing this infinite component it has less memory and storage req...

The problem of sampling from a given distribution on high-dimensional continuous spaces arises in the computational sciences and Bayesian statistics, and a frequentlyused solution is Markov chain Monte Carlo (MCMC); see [13] for many examples. Because MCMC methods produce good samples only after a lengthy mixing period, a long-standing mathematical question is to analyze the mixing times of the...