Variational Bayes and the reduced dependence approximation for the autologistic model on an irregular grid with applications

McGrory, Clare A., Pettitt, Anthony N., Reeves, Robert, Griffin, Mark and Dwyer, Mark (2012) Variational Bayes and the reduced dependence approximation for the autologistic model on an irregular grid with applications. Journal of Computational and Graphical Statistics, 21 3: 781-796.

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Author McGrory, Clare A.
Pettitt, Anthony N.
Reeves, Robert
Griffin, Mark
Dwyer, Mark
Total Author Count Override 5
Title Variational Bayes and the reduced dependence approximation for the autologistic model on an irregular grid with applications
Journal name Journal of Computational and Graphical Statistics  (ERA 2012 Listed)    (ERA 2010 Rank A*)   Check publisher's open access policy
Publication date 2012
Sub-type Article
Year available 2011
DOI 10.1080/10618600.2012.632232
Volume number 21
Issue number 3
ISSN 1061-8600
1537-2715
Start page 781
End page 796
Total pages 16
Place of publication Baltimore, MD, U.S.A.
Publisher American Statistical Association
Collection year 2013
Language eng
Formatted abstract Discrete Markov random field models provide a natural framework for representing images or spatial datasets. They model the spatial association present while providing a convenient Markovian dependency structure and strong edge-preservation properties. However, parameter estimation for discrete Markov random field models is difficult due to the complex form of the associated normalizing constant for the likelihood function. For large lattices, the reduced dependence approximation to the normalizing constant is based on the concept of performing computationally efficient and feasible forward recursions on smaller sublattices which are then suitably combined to estimate the constant for the whole lattice. We present an efficient computational extension of the forward recursion approach for the autologistic model to lattices that have an irregularly shaped boundary and which may contain regions with no data; these lattices are typical in applications. Consequently, we also extend the reduced dependence approximation to these scenarios enabling us to implement a practical and efficient non-simulation based approach for spatial data analysis within the variational Bayesian framework. The methodology is illustrated through application to simulated data and example images. The supplemental materials include our C++ source code for computing the approximate normalizing constant and simulation studies.
Keyword Variational Bayes
Discrete Markov random field modeling
Reduced dependence approximation
Bayesian analysis
Image analysis
Spatial data
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article
Collections: School of Mathematics and Physics
Official 2013 Collection
School of Population Health Publications
 
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Created: Tue, 24 Jan 2012, 14:23:40 EST by Kay Mackie on behalf of School of Mathematics & Physics