Spatially correlated allocation models for count data
Peter J. Green (Bristol)
Sylvia Richardson (Imperial College, London)
Spatial heterogeneity of count data on a rare phenomenon
occurs commonly in many domains of application, in particularly
in disease mapping. We present new
methodology to analyse such data, based on a
hierarchical allocation model. We assume that the
counts follow a Poisson model at the lowest level of the hierarchy,
and introduce a finite mixture model for the Poisson rates at the
next level. The novelty lies in the allocation model
to the mixture components, which follows a spatially correlated
process, the Potts model, and in treating the
number of components of the spatial mixture as unknown. Inference is
performed in a Bayesian framework using
reversible jump MCMC. The model introduced
can be viewed as a Bayesian semiparametric approach to
specifying flexible spatial distribution in hierarchical models.
It could also be used in contexts where the spatial mixture subgroups
are themselves of interest, as in health care monitoring.
Performance of the model and comparison with
an alternative well-known
Markov random field model specification for the Poisson rates
are demonstrated on synthetic data sets.
We found that our allocation model avoids the problem of
oversmoothing in cases where the underlying rates exhibit
discontinuities, while giving equally good results in cases
of smooth gradient-like or highly autocorrelated rates.
The methodology is illustrated on epidemiological applications to
data on rare disease and health outcome in France.
Some key words:
Bayesian hierarchical model,
Finite mixture distributions,
Markov chain Monte Carlo,
Reversible jump algorithms,
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