Efficient recursions for general factorisable models

Reeves, Robert W.; Pettitt, Anthony N.

doi:10.1093/biomet/91.3.751

Cited by 44 publications

(55 citation statements)

References 19 publications

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“…In our analysis of the soil phosphate dataset, discussed in Sect. 5.2, we also compare our results with those obtained using the auxiliary variable MCMC approach of Møller et al (2006) and the recursive method of Reeves and Pettitt (2004).…”

Section: Introductionmentioning

confidence: 93%

“…The RDA (Friel et al 2008) extends the recursion method for normalising constant calculation, presented in Reeves and Pettitt (2004), to problems involving larger lattices. This results in an approximation to the true normalising constant.…”

Section: The Reduced Dependence Approximationmentioning

confidence: 99%

“…This results in an approximation to the true normalising constant. The recursive method (Reeves and Pettitt 2004) enables exact computation of the normalising constant for an unnormalised joint likelihood that can be expressed as a product of factors. As factorisation of the joint likelihood is applicable to any discrete Markov random field, the recursion method is suitable for these models.…”

Section: The Reduced Dependence Approximationmentioning

confidence: 99%

“…Approaches include approximate methods such as thermodynamic integration, or path sampling (Gelman and Meng 1998;Pettitt et al 2003). Reeves and Pettitt (2004) present an exact recursive method which enables calculation of the normalising constant for small lattices and this is extended in Friel et al (2008) for application to larger lattices through an approximate method called the Reduced Dependence Approximation or RDA.…”

Section: Introductionmentioning

confidence: 99%

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Variational Bayes for estimating the parameters of a hidden Potts model

et al. 2008

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Hidden Markov random field models provide an appealing representation of images and other spatial problems. The drawback is that inference is not straightforward for these models as the normalisation constant for the likelihood is generally intractable except for very small observation sets. Variational methods are an emerging tool for Bayesian inference and they have already been successfully applied in other contexts. Focusing on the particular case of a hidden Potts model with Gaussian noise, we show how variational Bayesian methods can be applied to hidden Markov random field inference. To tackle the obstacle of the intractable normalising constant for the likelihood, we explore alternative estimation approaches for incorporation into the variational Bayes algorithm. We consider a pseudolikelihood approach as well as the more recent reduced dependence approximation of the normalisation constant. To illustrate the effectiveness of these approaches we present empirical results from the analysis of simulated datasets. We also analyse a real dataset and compare results with those of previous analyses as well as those obtained from the recently developed auxiliary variable MCMC method and the recursive MCMC method. Our results show that the variational Bayesian analyses can be carried out much faster than the MCMC analyses and produce good estimates of model parameters. We also found that the reduced dependence approximation of the normalisation constant outperformed the

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Section: Introductionmentioning

confidence: 93%

Section: The Reduced Dependence Approximationmentioning

confidence: 99%

Section: The Reduced Dependence Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Variational Bayes for estimating the parameters of a hidden Potts model

et al. 2008

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“…MRFs can similarly be updated by forward-backward algorithms, see e.g. Reeves and Pettitt (2004) and H. Tjelmeland and Austad (2012).…”

Section: Notation and Modeling Assumptionsmentioning

confidence: 99%

Dynamic exploration designs for graphical models using clustering with applications to petroleum exploration

Martinelli

Eidsvik

2014

Knowledge-Based Systems

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The paper considers the problem of optimal sequential design for graphical models. The joint probability model for all node variables is considered known. As data is collected, this probability model is updated. The sequential design problem entails a dynamic selection of nodes for data collection. The goal is to maximize utility, here defined via entropy or total profit. With a large number of nodes, the optimal solution to this selection problem is not tractable. Here, an approximation based on a subdivision of the graph is considered. Within the smaller clusters the design problem can be solved exactly. The results on clusters are combined in a dynamic manner, to create sequential designs for the entire graph. The merging of clusters also gives upper bounds for the actual value of the strategy. Several synthetic models are studied, along with two real cases from the oil and gas industry. In these examples Bayesian networks or Markov random fields are used. The sequential model updating and data collection guided by cluster values can provide useful guidelines to policy makers.

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Hidden Gibbs random fields model selection using Block Likelihood Information Criterion

Stoehr

Marin

Pudlo

2016

Stat

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Performing model selection between Gibbs random fields is a very challenging task. Indeed, due to the Markovian dependence structure, the normalizing constant of the fields cannot be computed using standard analytical or numerical methods. Furthermore, such unobserved fields cannot be integrated out and the likelihood evaluztion is a doubly intractable problem. This forms a central issue to pick the model that best fits an observed data. We introduce a new approximate version of the Bayesian Information Criterion. We partition the lattice into continuous rectangular blocks and we approximate the probability measure of the hidden Gibbs field by the product of some Gibbs distributions over the blocks. On that basis, we estimate the likelihood and derive the Block Likelihood Information Criterion (BLIC) that answers model choice questions such as the selection of the dependency structure or the number of latent states. We study the performances of BLIC for those questions. In addition, we present a comparison with ABC algorithms to point out that the novel criterion offers a better trade-off between time efficiency and reliable results.

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Efficient recursions for general factorisable models

Cited by 44 publications

References 19 publications

Variational Bayes for estimating the parameters of a hidden Potts model

Variational Bayes for estimating the parameters of a hidden Potts model

Dynamic exploration designs for graphical models using clustering with applications to petroleum exploration

Hidden Gibbs random fields model selection using Block Likelihood Information Criterion

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