Statistical Modelling 7 (2007), 275–295
Statistical modelling using product partition models
Claire Jordan
Institute of Information and Mathematical Sciences,
Massey University,
Private Bag, 102 904 NSMC,
Auckland
New Zealand.
eMail:
C.A.Jordan@massey.ac.nz
Vicki Livingstone
Department of Preventive and Social Medicine,
University of Otago,
Dunedin
New Zealand
Daniel Barry
Department of Mathematics and Statistics,
University of Limerick,
Limerick
Ireland
Abstract:
Product partition models (PPMs) allow us to partition a set of
objects into k sets. PPMs are a special case of Bayesian Partition
models. They use partially exchangeable priors where given a
partition ρ of the objects into k sets, the objects in the
same set are exchangeable and the objects belonging to distinct
sets are independent. PPMs specify prior probabilities for a
random partition and update these into posterior distributions
of the same form. They provide a convenient way of allowing the
data to weight the partitions likely to hold. Posterior estimates
of the parameter of interest are obtained by conditioning on the
partition and averaging over all generated partitions. Markov
chain Monte Carlo (MCMC) techniques are used to generate
partitions of the data. PPMs can be applied to many diverse e
stimation problems and in this paper we outline two areas where
they are useful
Keywords:
meta-analysis; prediction; product partition models
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