Results 1  10
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85
Bayesian Analysis of Mixture Models with an Unknown Number of Components  an alternative to reversible jump methods
, 1998
"... Richardson and Green (1997) present a method of performing a Bayesian analysis of data from a finite mixture distribution with an unknown number of components. Their method is a Markov Chain Monte Carlo (MCMC) approach, which makes use of the "reversible jump" methodology described by Gree ..."
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Cited by 114 (0 self)
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Richardson and Green (1997) present a method of performing a Bayesian analysis of data from a finite mixture distribution with an unknown number of components. Their method is a Markov Chain Monte Carlo (MCMC) approach, which makes use of the "reversible jump" methodology described by Green (1995). We describe an alternative MCMC method which views the parameters of the model as a (marked) point process, extending methods suggested by Ripley (1977) to create a Markov birthdeath process with an appropriate stationary distribution. Our method is easy to implement, even in the case of data in more than one dimension, and we illustrate it on both univariate and bivariate data. Keywords: Bayesian analysis, Birthdeath process, Markov process, MCMC, Mixture model, Model Choice, Reversible Jump, Spatial point process 1 Introduction Finite mixture models are typically used to model data where each observation is assumed to have arisen from one of k groups, each group being suitably modelle...
Estimating Recombination Rates from Population Genetic Data
, 2000
"... We introduce a new method for estimating recombination rates from population genetic data. The method uses a computationallyintensive statistical procedure (importance sampling) to calculate the likelihood under a coalescentbased model. Detailed comparisons of the new algorithm with two existing m ..."
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Cited by 90 (11 self)
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We introduce a new method for estimating recombination rates from population genetic data. The method uses a computationallyintensive statistical procedure (importance sampling) to calculate the likelihood under a coalescentbased model. Detailed comparisons of the new algorithm with two existing methods (one based on importance sampling and one based on MCMC) show it to be substantially more efficient. (The improvement over the existing importance sampling scheme is typically by four orders of magnitude.) The existing approaches not infrequently led to misleading results on the problems we investigated. We also performed a simulation study to look at the properties of the maximum likelihood estimator (mle) of the recombination rate, and its robustness to misspecification of the demographic model.
Bayesian sparse hidden components analysis for transcription regulation networks
, 2005
"... Motivation: In systems like E. Coli, the abundance of sequence information, gene expression array studies, and small scale experiments allows one to reconstruct the regulatory network and to quantify the effects of transcription factors on gene expression. However, this goal can only be achieved if ..."
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Cited by 40 (1 self)
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Motivation: In systems like E. Coli, the abundance of sequence information, gene expression array studies, and small scale experiments allows one to reconstruct the regulatory network and to quantify the effects of transcription factors on gene expression. However, this goal can only be achieved if all information sources are used in concert. Results: Our method integrates literature information, DNA sequences, and expression arrays. A set of relevant transcription factors is defined on the basis of literature. Sequence data is used to identify potential target genes and the results are used to define a prior distribution on the topology of the regulatory network. A Bayesian hidden component model for the expression array data allows us to identify which of the potential binding sites are actually used by the regulatory proteins in the studied cell conditions, the strength of their control, and their activation profile in a series of experiments. We apply our methodology to 35 expression studies in E. Coli with convincing results. Availability: www.genetics.ucla.edu/labs/sabatti/software.html
Parallel computing and Monte Carlo algorithms
, 1999
"... We argue that Monte Carlo algorithms are ideally suited to parallel computing, and that "parallel Monte Carlo" should be more widely used. We consider a number of issues that arise, including dealing with slow or unreliable computers. We also discuss the possibilities of parallel Markov ch ..."
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Cited by 38 (0 self)
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We argue that Monte Carlo algorithms are ideally suited to parallel computing, and that "parallel Monte Carlo" should be more widely used. We consider a number of issues that arise, including dealing with slow or unreliable computers. We also discuss the possibilities of parallel Markov chain Monte Carlo. We illustrate our results with actual computer experiments.
Hyperparameter estimation for satellite image restoration using a MCMC Maximum Likelihood method
 Pattern Recognition
, 2000
"... The satellite image deconvolution problem is illposed and must be regularized. Herein, we use an edgepreserving regularization model using a ' function, involving two hyperparameters. Our goal is to estimate the optimal parameters in order to automatically reconstruct images. We propose to us ..."
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Cited by 37 (10 self)
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The satellite image deconvolution problem is illposed and must be regularized. Herein, we use an edgepreserving regularization model using a ' function, involving two hyperparameters. Our goal is to estimate the optimal parameters in order to automatically reconstruct images. We propose to use the Maximum Likelihood Estimator (MLE), applied to the observed image. We need sampling from prior and posterior distributions. Since the convolution prevents from using standard samplers, we have developed a modied GemanYang algorithm, using an auxiliary variable and a cosine transform. We present a Markov Chain Monte Carlo Maximum Likelihood (MCMCML) technique which is able to simultaneously achieve the estimation and the reconstruction.
Possible biases induced by MCMC convergence diagnostics
, 1997
"... This paper is organised as follows. In Section 2, we present an oversimplified version of a convergence diagnostic, and study analytically its performance on certain simple Markov chains. We restrict ourselves primarily to chains which in fact produce i.i.d. samples from ..."
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Cited by 22 (2 self)
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This paper is organised as follows. In Section 2, we present an oversimplified version of a convergence diagnostic, and study analytically its performance on certain simple Markov chains. We restrict ourselves primarily to chains which in fact produce i.i.d. samples from
Markov Chain Monte Carlo and Spatial Point Processes
, 1999
"... this paper) reversibility holds, that is f P(x, A)(,x) = f PC, B A for all A, B , whereby r is clearly invariant ..."
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Cited by 20 (5 self)
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this paper) reversibility holds, that is f P(x, A)(,x) = f PC, B A for all A, B , whereby r is clearly invariant
The stochastic EM algorithm: Estimation and asymptotic results
, 2000
"... The EM algorithm (Dempster, Laird, and Rubin (1978)) is a much used tool for maximum likelihood estimation in missing or incomplete data problems. However, calculating the conditional expectation required in the Estep of the algorithm may be infeasible, especially when this expectation is a large s ..."
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Cited by 19 (0 self)
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The EM algorithm (Dempster, Laird, and Rubin (1978)) is a much used tool for maximum likelihood estimation in missing or incomplete data problems. However, calculating the conditional expectation required in the Estep of the algorithm may be infeasible, especially when this expectation is a large sum or a highdimensional integral. Instead an estimate of the expectation can be formed by simulation. This is the common idea in the stochastic EM algorithm (Celeux and Diebolt (1986)) and the Monte Carlo EM algorithm (Wei and Tanner (1990)). In this paper some asymptotic results for the stochastic EM algorithm are given, and estimation based on the stochastic EM algorithm is discussed. In particular, asymptotic equivalence of certain simple estimators is shown, and a simulation experiment is carried out to investigate this equivalence in small and moderate samples. Furthermore, some implementation issues and the possibility of allowing unidentified parameters in the algorithm are discussed.
Convergence Assessment for Reversible Jump MCMC Simulations
, 1998
"... In this paper we introduce the problem of assessing convergence of reversible jump MCMC algorithms on the basis of simulation output. We discuss the various direct approaches which could be employed, together with their associated drawbacks. Using the example of fitting a graphical Gaussian model vi ..."
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Cited by 18 (0 self)
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In this paper we introduce the problem of assessing convergence of reversible jump MCMC algorithms on the basis of simulation output. We discuss the various direct approaches which could be employed, together with their associated drawbacks. Using the example of fitting a graphical Gaussian model via RJMCMC, we show how the simulation output for models which can be parameterised so that parameters of primary interest retain a coherent interpretation throughout the simulation, can be used to assess convergence. In the context of this example, we extend the work of Gelman and Rubin (1992) and Brooks and Gelman (1998), to provide convergence assessment procedures for graphical model determination problems, but which may be applied to any form of model choice problem and, indeed, MCMC simulations more generally.