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An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants
 Biometrika
, 2006
"... Maximum likelihood parameter estimation and sampling from Bayesian posterior distributions are problematic when the probability density for the parameter of interest involves an intractable normalising constant which is also a function of that parameter. In this paper, an auxiliary variable method i ..."
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Cited by 49 (2 self)
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Maximum likelihood parameter estimation and sampling from Bayesian posterior distributions are problematic when the probability density for the parameter of interest involves an intractable normalising constant which is also a function of that parameter. In this paper, an auxiliary variable method is presented which requires only that independent samples can be drawn from the unnormalised density at any particular parameter value. The proposal distribution is constructed so that the normalising constant cancels from the Metropolis–Hastings ratio. The method is illustrated by producing posterior samples for parameters of the Ising model given a particular lattice realisation.
Smoothing algorithms for statespace models
 in Submission IEEE Transactions on Signal Processing
, 2004
"... A prevalent problem in statistical signal processing, applied statistics, and time series analysis is the calculation of the smoothed posterior distribution, which describes the uncertainty associated with a state, or a sequence of states, conditional on data from the past, the present, and the futu ..."
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Cited by 30 (4 self)
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A prevalent problem in statistical signal processing, applied statistics, and time series analysis is the calculation of the smoothed posterior distribution, which describes the uncertainty associated with a state, or a sequence of states, conditional on data from the past, the present, and the future. The aim of this paper is to provide a rigorous foundation for the calculation, or approximation, of such smoothed distributions, to facilitate a robust and efficient implementation. Through a cohesive and generic exposition of the scientific literature we offer several novel extensions such that one can perform smoothing in the most general case. Experimental results for: a Jump Markov Linear System; a comparison of particle smoothing methods; and parameter estimation using a particle implementation of the EM algorithm, are provided.
Markov chain Monte Carlo methods for statistical inference
, 2004
"... These notes provide an introduction to Markov chain Monte Carlo methods and their applications to both Bayesian and frequentist statistical inference. Such methods have revolutionized what can be achieved computationally, especially in the Bayesian paradigm. The account begins by discussing ordinary ..."
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Cited by 7 (0 self)
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These notes provide an introduction to Markov chain Monte Carlo methods and their applications to both Bayesian and frequentist statistical inference. Such methods have revolutionized what can be achieved computationally, especially in the Bayesian paradigm. The account begins by discussing ordinary Monte Carlo methods: these have the same goals as the Markov chain versions but can only rarely be implemented. Subsequent sections describe basic Markov chain Monte Carlo, based on the Hastings algorithm and including both the Metropolis method and the Gibbs sampler as special cases, and go on to discuss some more specialized developments, including adaptive slice sampling, exact goodness–of–fit tests, maximum likelihood estimation, the Langevin–Hastings algorithm, auxiliary variables techniques, perfect sampling via coupling from the past, reversible jumps methods for target spaces of varying dimensions, and simulated annealing. Specimen applications are described throughout the notes.
Bayesian Multivariate Isotonic Regression Splines: Applications to Carcinogenicity Studies
"... In many applications, interest focuses on assessing the relationship between a predictor and a multivariate outcome variable, and there may be prior knowledge about the shape of the regression curves. For example, regression functions relating dose of a possible risk factor to different adverse outc ..."
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Cited by 1 (0 self)
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In many applications, interest focuses on assessing the relationship between a predictor and a multivariate outcome variable, and there may be prior knowledge about the shape of the regression curves. For example, regression functions relating dose of a possible risk factor to different adverse outcomes can often be assumed to be nondecreasing. In such cases, interest focuses on (1) assessing evidence of an overall adverse effect; (2) determining which outcomes are most affected; and (3) estimating outcomespecific regression curves. This article proposes a Bayesian approach for addressing this problem, motivated by multisite tumor data from carcinogenicity experiments. A multivariate smoothing spline model is specified, which accommodates dependency in the multiple curves through a hierarchical Markov random field prior for the basis coefficients, while also allowing for residual correlation. A Gibbs sampler is proposed for posterior computation, and the approach is applied to data on body weight and tumor occurrence.
Efficient recursions for general factorisable models
"... Let n Svalued categorical variables be jointly distributed according to a distribution known only up to an unknown normalising constant. For an unnormalised joint likelihood expressible as a product of factors, we give an algebraic recursion which can be used for computing the normalising constant ..."
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Let n Svalued categorical variables be jointly distributed according to a distribution known only up to an unknown normalising constant. For an unnormalised joint likelihood expressible as a product of factors, we give an algebraic recursion which can be used for computing the normalising constant and other summations. A saving in computation is achieved when each factor contains a lagged subset of the components combining in the joint distribution, with maximum computational efficiency as the subsets attain their minimum size. If each subset contains at most r + 1 of the n components in the joint distribution, we term this a lagr model, whose normalising constant can be computed using a forward recursion in O(S r+1) computations, as opposed to O(S n) for the direct computation. We show how a lagr model represents a Markov random field and allows a neighbourhood structure to be related to the unnormalised joint likelihood. We illustrate the method by showing how the normalising constant of the Ising or autologistic model can be computed.
(PE/CIMAT) A Case Study: Ordinal Responses With SpatioTemporal Dependencies
"... Abstract: Data structures with spatial and temporal dependencies are not uncommon in environmental and agronomic fields. We consider the modeling and estimation problem for these type of structures, in particular we consider proportional odds models with spatiotemporal covariables with estimation v ..."
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Abstract: Data structures with spatial and temporal dependencies are not uncommon in environmental and agronomic fields. We consider the modeling and estimation problem for these type of structures, in particular we consider proportional odds models with spatiotemporal covariables with estimation via maximum pseudlikelihood. We end by presenting a testing problem on treatment effects on data from a field experiment on agave tequilana.
Summary
, 2009
"... Maximum likelihood parameter estimation is frequently replaced by various techniques because of its intractable normalizing constant. In the same way, the literature displays various alternatives for distributions involving such unreachable constants. In this paper, we consider a Gibbs distribution ..."
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Maximum likelihood parameter estimation is frequently replaced by various techniques because of its intractable normalizing constant. In the same way, the literature displays various alternatives for distributions involving such unreachable constants. In this paper, we consider a Gibbs distribution π and present a recurrence formula allowing a recursive calculus of the marginals of π and in the same time its normalizing constant. The numerical performance of this algorithm is evaluated for several examples, particularly for an Ising model on a lattice.
Statistics Exact marginals and normalizing constant for Gibbs distributions
, 2013
"... We present a recursive algorithm for the calculation of the marginal of a Gibbs distribution π. A direct consequence is the calculation of the normalizing constant of π. Résumé Récurrences et constante de normalisation pour des modèles de Gibbs. Nous proposons dans ce travail une récurrence sur les ..."
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We present a recursive algorithm for the calculation of the marginal of a Gibbs distribution π. A direct consequence is the calculation of the normalizing constant of π. Résumé Récurrences et constante de normalisation pour des modèles de Gibbs. Nous proposons dans ce travail une récurrence sur les lois marginales d’une distribution de Gibbs π. Une conséquence directe est le calcul exact de la constante de normalisation de π. 1.