Bayesian multivariate Poisson mixtures with an unknown number of components |
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Authors: | Loukia Meligkotsidou |
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Institution: | (1) Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, UK |
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Abstract: | In this paper we present Bayesian analysis of finite mixtures of multivariate Poisson distributions with an unknown number
of components. The multivariate Poisson distribution can be regarded as the discrete counterpart of the multivariate normal
distribution, which is suitable for modelling multivariate count data. Mixtures of multivariate Poisson distributions allow
for overdispersion and for negative correlations between variables. To perform Bayesian analysis of these models we adopt
a reversible jump Markov chain Monte Carlo (MCMC) algorithm with birth and death moves for updating the number of components.
We present results obtained from applying our modelling approach to simulated and real data. Furthermore, we apply our approach
to a problem in multivariate disease mapping, namely joint modelling of diseases with correlated counts. |
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Keywords: | Bayesian inference Disease mapping Mixture models Multivariate Poisson distribution Reversible jump MCMC |
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