Related papers: Consistent estimation of the basic neighborhood of…
The present paper has two goals. First to present a natural example of a new class of random fields which are the variable neighborhood random fields. The example we consider is a partially observed nearest neighbor binary Markov random…
The Markov chain random field (MCRF) model/theory provides a non-linear spatial Bayesian updating solution at the neighborhood nearest data level for simulating categorical spatial variables. In the MCRF solution, the spatial dependencies…
We consider random fields defined by finite-region conditional probabilities depending on a neighborhood of the region which changes with the boundary conditions. To predict the symbols within any finite region it is necessary to inspect a…
Discrete Markov random fields are undirected graphical models that capture complex conditional dependencies between discrete variables. Conducting exact posterior inference in these models is often computationally challenging because…
Discrete Markov random fields form a natural class of models to represent images and spatial data sets. The use of such models is, however, hampered by a computationally intractable normalising constant. This makes parameter estimation and…
It was shown many times in the literature that a Markov random field is equivalent to a Gibbs random field when all realizations of the field have non-zero probabilities; the proofs are rather complicated. A simpler proof, which is based…
We show that the definition of neighbor in Markov random fields as defined by Besag (1974) when the joint distribution of the sites is not positive is not well-defined. In a random field with finite number of sites we study the conditions…
In this paper, we show that the methods of mathematical statistical physics can be successfully applied to random fields in finite volumes. As a result, we obtain simple necessary and sufficient conditions for the existence and uniqueness…
A number of problems in statistical physics and computer science can be expressed as the computation of marginal probabilities over a Markov random field. Belief propagation, an iterative message-passing algorithm, computes exactly such…
Developing satisfactory methodology for the analysis of Markov random field is a very challenging task. Indeed, due to the Markovian dependence structure, the normalizing constant of the fields cannot be computed using standard analytical…
In this paper we discuss a method, which we call Minimum Conditional Description Length (MCDL), for estimating the parameters of a subset of sites within a Markov random field. We assume that the edges are known for the entire graph…
This paper considers a Bayesian view for estimating a sub-network in a Markov random field. The sub-network corresponds to the Markov blanket of a set of query variables, where the set of potential neighbours here is big. We factorize the…
Stochastic parameterisations deployed in models of the Earth system frequently invoke locality assumptions such as Markovianity or spatial locality. This work highlights the impact of such assumptions on predictive performance. Both in…
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.…
Bounding the optimal precision in parameter estimation tasks is of central importance for technological applications. In the regime of a small number of measurements, or that of low signal-to-noise ratios, the meaning of common frequentist…
We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. The benchmark information-theoretic results in the case of d-regular graphs require the number of samples to be at least proportional to…
Markov random fields area popular model for high-dimensional probability distributions. Over the years, many mathematical, statistical and algorithmic problems on them have been studied. Until recently, the only known algorithms for…
Variational approximation has been widely used in large-scale Bayesian inference recently, the simplest kind of which involves imposing a mean field assumption to approximate complicated latent structures. Despite the computational…
The empirical Bayes estimators in mixed models are useful for small area estimation in the sense of increasing precision of prediction for small area means, and one wants to know the prediction errors of the empirical Bayes estimators based…
We propose a penalized pseudo-likelihood criterion to estimate the graph of conditional dependencies in a discrete Markov random field that can be partially observed. We prove the convergence of the estimator in the case of a finite or…