2,828 research outputs found
Kalikow-type decomposition for multicolor infinite range particle systems
We consider a particle system on with real state space and
interactions of infinite range. Assuming that the rate of change is continuous
we obtain a Kalikow-type decomposition of the infinite range change rates as a
mixture of finite range change rates. Furthermore, if a high noise condition
holds, as an application of this decomposition, we design a feasible perfect
simulation algorithm to sample from the stationary process. Finally, the
perfect simulation scheme allows us to forge an algorithm to obtain an explicit
construction of a coupling attaining Ornstein's -distance for two
ordered Ising probability measures.Comment: Published in at http://dx.doi.org/10.1214/12-AAP882 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Multiple Testing for Neuroimaging via Hidden Markov Random Field
Traditional voxel-level multiple testing procedures in neuroimaging, mostly
-value based, often ignore the spatial correlations among neighboring voxels
and thus suffer from substantial loss of power. We extend the
local-significance-index based procedure originally developed for the hidden
Markov chain models, which aims to minimize the false nondiscovery rate subject
to a constraint on the false discovery rate, to three-dimensional neuroimaging
data using a hidden Markov random field model. A generalized
expectation-maximization algorithm for maximizing the penalized likelihood is
proposed for estimating the model parameters. Extensive simulations show that
the proposed approach is more powerful than conventional false discovery rate
procedures. We apply the method to the comparison between mild cognitive
impairment, a disease status with increased risk of developing Alzheimer's or
another dementia, and normal controls in the FDG-PET imaging study of the
Alzheimer's Disease Neuroimaging Initiative.Comment: A MATLAB package implementing the proposed FDR procedure is available
with this paper at the Biometrics website on Wiley Online Librar
Julian Ernst Besag, 26 March 1945 -- 6 August 2010, a biographical memoir
Julian Besag was an outstanding statistical scientist, distinguished for his
pioneering work on the statistical theory and analysis of spatial processes,
especially conditional lattice systems. His work has been seminal in
statistical developments over the last several decades ranging from image
analysis to Markov chain Monte Carlo methods. He clarified the role of
auto-logistic and auto-normal models as instances of Markov random fields and
paved the way for their use in diverse applications. Later work included
investigations into the efficacy of nearest neighbour models to accommodate
spatial dependence in the analysis of data from agricultural field trials,
image restoration from noisy data, and texture generation using lattice models.Comment: 26 pages, 14 figures; minor revisions, omission of full bibliograph
Bayesian Parameter Estimation for Latent Markov Random Fields and Social Networks
Undirected graphical models are widely used in statistics, physics and
machine vision. However Bayesian parameter estimation for undirected models is
extremely challenging, since evaluation of the posterior typically involves the
calculation of an intractable normalising constant. This problem has received
much attention, but very little of this has focussed on the important practical
case where the data consists of noisy or incomplete observations of the
underlying hidden structure. This paper specifically addresses this problem,
comparing two alternative methodologies. In the first of these approaches
particle Markov chain Monte Carlo (Andrieu et al., 2010) is used to efficiently
explore the parameter space, combined with the exchange algorithm (Murray et
al., 2006) for avoiding the calculation of the intractable normalising constant
(a proof showing that this combination targets the correct distribution in
found in a supplementary appendix online). This approach is compared with
approximate Bayesian computation (Pritchard et al., 1999). Applications to
estimating the parameters of Ising models and exponential random graphs from
noisy data are presented. Each algorithm used in the paper targets an
approximation to the true posterior due to the use of MCMC to simulate from the
latent graphical model, in lieu of being able to do this exactly in general.
The supplementary appendix also describes the nature of the resulting
approximation.Comment: 26 pages, 2 figures, accepted in Journal of Computational and
Graphical Statistics (http://www.amstat.org/publications/jcgs.cfm
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