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RESEARCH ARTICLE
Contents Vol 56(4)

Extending the Bayesian mixture model to incorporate spatial information in analysing sheep CAT scan images

C. L. Alston A E , K. L. Mengersen B , J. M. Thompson C , P. J. Littlefield C , D. Perry C and A. J. Ball D
+ Author Affiliations
- Author Affiliations

A School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia.

B School of Mathematical Sciences, Queensland University of Technology, Brisbane, Qld 4001, Australia.

C Co-operative Research Centre for the Cattle and Beef Industries, University of New England, Armidale, NSW 2351, Australia.

D Meat and Livestock Australia, University of New England, Armidale, NSW 2351, Australia.

E Corresponding author. Email: clair.alston@studentmail.newcastle.edu.au

Australian Journal of Agricultural Research 56(4) 373-388 https://doi.org/10.1071/AR04211
Submitted: 7 September 2004  Accepted: 17 February 2005   Published: 26 April 2005

Abstract

The purpose of CAT scanning in some animal science experiments is to provide estimates of the proportion of the tissues, fat, muscle, and bone present in an individual body, and compare some of the density characteristics.

In this paper we present an extension to the hierarchical Bayesian Normal mixture model, which incorporates some of the information provided by the neighbouring pixels in a CAT scan image. This neighbour information is included in the model through the use of a Markov random field for the component allocation variable. This extended mixture model provides a more responsive fit to the local likelihood of the data than that of the independent mixture model.

The effectiveness of this modelling technique is illustrated by comparing its performance with that of a Normal mixture model and a fixed boundary method in 3 examples. In these examples it is shown that the extended mixture model we propose is most useful in situations that involve only slight separation of components. The advantages of the model decline as the separation of components increases.

Additional keywords: density estimation, Gibbs sampling, Markov Chain Monte Carlo, Markov random field, Metropolis-Hastings algorithm, posterior simulation.


References


Alston CL, Mengersen KL, Thompson JM, Littlefield PJ, Perry D, Ball AJ (2004) Statistical analysis of sheep cat scan images using a Bayesian mixture model. Australian Journal of Agricultural Research 55, 57–68.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Ball AJ, Thompson JM, Alston CL, Blakely AR, Hinch GN (1998) Changes in maintenance energy requirements of mature sheep fed at different levels of feed intake at maintenance, weight loss and realimentation. Livestock Production Science 53, 191–204.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Best NG, Cowles MK, Vines K (1995) Coda: Convergence Diagnosis and Output Analysis software for Gibbs sampling output, Version 0. 30. Technical Report, MRC Biostatistics Unit, University of Cambridge.

Carlin, BP ,  and  Louis, TA (2000). ‘Bayes and Empirical Bayes methods for data analysis.’ 2nd edn . (Chapman and Hall/CRC: New York)

Fernández C, Green PJ (2002) Modelling spatially correlated data via mixtures: a Bayesian approach. Journal of the Royal Statistical Society: Series B 64, 805–826.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Glasbey CA, Robinson CD (2002) Estimators of tissue proportions from X-ray CT images. Biometrics 58, 928–936.
| Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Gruet MA, Philippe A, Robert CP (1998) Estimation of exponential mixtures. ‘Discretization and MCMC convergence assessment’. (Ed. CP Robert) pp. 161–173. (Springer-Verlag: New York)

Jopson NB, Thompson JM, Fennessy PF (1997) Tissue mobilisation rates in male fallow deer (Dama dama) as determined by Computed Tomography: the effects of natural and enforced food restriction. Animal Science 65, 311–320. open url image1

Kass RE, Raftery AE (1995) Bayes factors. Journal of the American Statistical Association 90, 773–795. open url image1

McLachlan, G ,  and  Peel, D (2000). ‘Finite mixture models.’ (John Wiley and Sons Ltd: New York)

Philippe A, Robert CP (1998) Linking discrete and continuous chains. ‘Discretization and MCMC convergence assessment’. (Ed. CP Robert) pp. 47–97. (Springer-Verlag: New York)

Potts RB (1952) Some generalized order-disorder transitions. Proceedings of the Cambridge Philosophical Society 48, 106–109. open url image1

R Development Core Team (2003). ‘R: A language and environment for statistical computing.’ (R Foundation for Statistical Computing: Vienna, Austria) Available at http://www.R-project.org

Richardson S, Green PJ (1997) On Bayesian analysis of mixtures with an unknown number of components (with discussion). Journal of the Royal Statistical Society: Series B 59, 731–792.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Robert, CP ,  and  Casella, G (1999). ‘Monte Carlo statistical methods.’ (Springer-Verlag: New York)

Rydén T, Titterington DM (1998) Computational Bayesian analysis of hidden Markov models. Journal of Computational and Graphical Statistics 7, 194–211. open url image1

Stanford D (1999) Fast automatic unsupervised image segmentation and curve detection in spatial point patterns. PhD thesis, University of Washington, USA.

Thompson J, Kinghorn B (1992) CATMAN—A program to measure CAT-Scans for prediction of body components in live animals. ‘Proceedings of the Australian Association of Animal Breeding and Genetics Vol. 10’. (AAAGB Distribution Service, The University of New England: Armidale, NSW)


Winkler, AH (2003). ‘Image analysis, random fields and Markov chain. Monte Carlo methods: a mathematical introduction.’ 2nd edn . (Springer-Verlag: Berlin, Germany)