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CATEGORIES:Statistics
SUMMARY:Bayesian Model Determination for Multivariate Ordi
nal and Binary Data - Jon Forster (University of S
outhampton)
DTSTART;TZID=Europe/London:20081107T160000
DTEND;TZID=Europe/London:20081107T170000
UID:TALK14323AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/14323
DESCRIPTION:We consider how to compare different conditional i
ndependence specifications\nfor ordinal categorica
l variables\, by calculating a posterior distribut
ion\nover classes of graphical models. The approac
h is based on the multivariate\nordinal probit mod
el (Chib and Greenberg\, 1998) where the data are\
nconsidered to have arisen as truncated multivaria
te normal random vectors.\nBy parameterising the p
recision matrix of the associated multivariate nor
mal\nin Cholesky form (e.g. as Smith and Kohn\, 20
02) ordinal data models\ncorresponding to directed
acyclic conditional independence graphs can be\ns
pecified and conveniently computed. Where one or m
ore of the variables is\nbinary this parameterisat
ion is particularly compelling\, as necessary\ncon
straints on the latent variable distribution can b
e imposed in such a way\nthat a standard\, fully n
ormalised\, prior can still be adopted. For\ncomp
aring different directed graphical models we propo
se a reversible jump\nMCMC approach. Where interes
t is focussed on undirected graphical models\,\nth
is approach is augmented to allow switches in the
orderings of variables\nof associated directed gra
phs\, hence allowing the posterior distribution\no
ver decomposable undirected graphical models to b
e computed. The approach\nis illustrated with seve
ral examples\, involving both binary and ordinal\n
variables\, and directed and undirected graphical
model classes.\n\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:
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