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A double MetropolisHastings sampler for spatial models with intractable normalizing constants
 Journal of Statistical Computing and Simulation
"... The problem of simulating from distributions with intractable normalizing constants has received much attention in the recent literature. In this paper, we propose an asymptotic algorithm, the socalled double MetropolisHastings (MH) sampler, for tickling this problem. Unlike other auxiliary variabl ..."
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Cited by 7 (2 self)
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The problem of simulating from distributions with intractable normalizing constants has received much attention in the recent literature. In this paper, we propose an asymptotic algorithm, the socalled double MetropolisHastings (MH) sampler, for tickling this problem. Unlike other auxiliary variable algorithms, the double MH sampler removes the need of exact sampling, the auxiliary variables being generated using MH kernels, and thus can be applied to a wide range of problems for which exact sampling is not available. While for the problems for which exact sampling is available, it can typically produce the same accurate results as the exchange algorithm, but using much less CPU time. The new method is illustrated by various spatial models.
Bayesian computation for statistical models with intractable normalizing constants
, 2008
"... normalizing constants ..."
Reconstructing the Energy Landscape of a Distribution from
"... Defining the energy function as the negative logarithm of the density, we explore the energy landscape of a distribution via the tree of sublevel sets of its energy. This tree represents the hierarchy among the connected components of the sublevel sets. We propose ways to annotate the tree so that i ..."
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Cited by 1 (0 self)
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Defining the energy function as the negative logarithm of the density, we explore the energy landscape of a distribution via the tree of sublevel sets of its energy. This tree represents the hierarchy among the connected components of the sublevel sets. We propose ways to annotate the tree so that it provides information on both topological and statistical aspects of the distribution, such as the local energy minima (local modes), their local domains and volumes, and the barriers between them. We develop a computational method to estimate the tree and reconstruct the energy landscape from Monte Carlo samples simulated at a wide energy range of a distribution. This method can be applied to any arbitrary distribution on a space with defined connectedness. We test the method on multimodal distributions and posterior distributions to show that our estimated trees are accurate compared to theoretical values. When used to perform Bayesian inference of DNA sequence segmentation, this approach reveals much more information than the standard approach based on marginal posterior distributions. Key words and phrases: Monte Carlo, cluster tree, sublevel set, connected component, disconnectivity graph, posterior distribution, sequence segmentation, change point. 1
RECONSTRUCTING THE ENERGY LANDSCAPE OF
"... Defining the energy function as the negative logarithm of the density, we explore the energy landscape of a distribution via the tree of sublevel sets of its energy. This tree represents the hierarchy among the connected components of the sublevel sets. We propose ways to annotate the tree so that i ..."
Abstract
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Defining the energy function as the negative logarithm of the density, we explore the energy landscape of a distribution via the tree of sublevel sets of its energy. This tree represents the hierarchy among the connected components of the sublevel sets. We propose ways to annotate the tree so that it provides information on both topological and statistical aspects of the distribution, such as the local energy minima (local modes), their local domains and volumes, and the barriers between them. We develop a computational method to estimate the tree and reconstruct the energy landscape from Monte Carlo samples simulated at a wide energy range of a distribution. This method can be applied to any arbitrary distribution on a space with defined connectedness. We test the method on multimodal distributions and posterior distributions to show that our estimated trees are accurate compared to theoretical values. When used to perform Bayesian inference of DNA sequence segmentation, this approach reveals much more information than the standard approach based on marginal posterior distributions. 1. Introduction. The
MRI Tissue Classification Using High Resolution Bayesian Hidden Markov Normal Mixture Models
, 2009
"... authors would like to thank Dr. Vincent Magnotta for helpful discussions and for making ..."
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authors would like to thank Dr. Vincent Magnotta for helpful discussions and for making
Use of SAMC for Bayesian Analysis of Statistical Models with Intractable Normalizing Constants
, 2010
"... Bayesian analysis for the models with intractable normalizing constants has attracted much attention in recent literature. In this paper, we propose a new algorithm, the socalled Bayesian Stochastic Approximation Monte Carlo (BSAMC) algorithm, for this problem. BSAMC provides an online approximati ..."
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Bayesian analysis for the models with intractable normalizing constants has attracted much attention in recent literature. In this paper, we propose a new algorithm, the socalled Bayesian Stochastic Approximation Monte Carlo (BSAMC) algorithm, for this problem. BSAMC provides an online approximation to the normalizing constant using the stochastic approximation Monte Carlo (SAMC) algorithm. One significant advantage of BSAMC over the auxiliary variable MCMC methods is that it avoids the requirement for perfect samples, and thus it can be applied to many models for which perfect sampling is impossible or very expensive. Although the normalizing constant approximation is also involved in BSAMC, as shown by our numerical examples, BSAMC can perform very robustly to initial guesses of parameters due to the powerful ability of SAMC in sample space exploration. Under mild conditions, we show that BSAMC estimates can converge almost surely to their true values. BSAMC also provides a general framework for approximate Bayesian sampling: sampling from a sequence of distributions for which the average of the logdensity functions converges to the true logdensity function.
Population Stochastic Approximation MCMC Algorithm and its Weak Convergence
, 2010
"... In this paper, we propose a population stochastic approximation MCMC (SAMCMC) algorithm, and establish its weak convergence (toward a normal distribution) under mild conditions. The theory of weak convergence established for the population SAMCMC algorithm is also applicable for general single chain ..."
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In this paper, we propose a population stochastic approximation MCMC (SAMCMC) algorithm, and establish its weak convergence (toward a normal distribution) under mild conditions. The theory of weak convergence established for the population SAMCMC algorithm is also applicable for general single chain SAMCMC algorithms. Based on the theory, we then give an explicit ratio for the convergence rates of the population SAMCMC algorithm and the single chain SAMCMC algorithm. The theoretical results are illustrated by a population stochastic approximation Monte Carlo (SAMC) algorithm with a multimodal example. Our results, in both theory and numerical examples, suggest that the population SAMCMC algorithm can be more efficient than the single chain SAMCMC algorithm. This is of interest for practical applications.