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SUMMARY:Bayesian Model Determination for Multivariate Ordinal and Binary D
 ata - Jon Forster (University of Southampton)
DTSTART:20081107T160000Z
DTEND:20081107T170000Z
UID:TALK14323@talks.cam.ac.uk
CONTACT:8419
DESCRIPTION:We consider how to compare different conditional independence 
 specifications\nfor ordinal categorical variables\, by calculating a poste
 rior distribution\nover classes of graphical models. The approach is based
  on the multivariate\nordinal probit model (Chib and Greenberg\, 1998) whe
 re the data are\nconsidered to have arisen as truncated multivariate norma
 l random vectors.\nBy parameterising the precision matrix of the associate
 d multivariate normal\nin Cholesky form (e.g. as Smith and Kohn\, 2002) or
 dinal data models\ncorresponding to directed acyclic conditional independe
 nce graphs can be\nspecified and conveniently computed. Where one or more 
 of the variables is\nbinary this parameterisation is particularly compelli
 ng\, as necessary\nconstraints on the latent variable distribution can be 
 imposed in such a way\nthat a standard\, fully normalised\, prior can stil
 l be adopted.  For\ncomparing different directed graphical models we propo
 se a reversible jump\nMCMC approach. Where interest is focussed on undirec
 ted graphical models\,\nthis approach is augmented to allow switches in th
 e orderings of variables\nof associated directed graphs\, hence allowing t
 he posterior distribution\nover  decomposable undirected graphical models 
 to be computed. The approach\nis illustrated with several examples\, invol
 ving both binary and ordinal\nvariables\, and directed and undirected grap
 hical model classes.\n\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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