Bayesian analysis of Poisson mixtures
Valerie Viallefont, Sylvia Richardson & Peter J. Green
The modelling of rare events via a Poisson distribution
sometimes reveals substantial over-dispersion,
indicating that some unexplained discontinuity arises in the data.
We suggest modelling this over-dispersion by a Poisson mixture.
In a hierarchical Bayesian model, the posterior distributions
of the unknown quantities of the mixture (number of components,
weights, and Poisson parameters) will be estimated by MCMC
algorithms, including the reversible jump algorithm which
permits varying the dimension between two states of the chain.
We will focus on the difficulty of finding a weakly
informative prior for the Poisson parameters distribution:
different priors will be detailed and compared.
Then the mixing performances of different moves created
for dimension change will be investigated.
The model is extended by the introduction of
covariates, whose effect can be either uniform or
different among the components.
Simulated data sets will be designed for the
different comparisons, and the model will finally
be illustrated on real data.
Some key words:
Reversible jump, Heterogeneity, Markov chain Monte Carlo,
Poisson mixtures, Priors
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