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Applied Bayesian Modelling, 2nd Edition by Peter Congdon

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2.5.2 Dirichlet process priors

Dirichlet Process Priors (abbreviated as DPP priors) offer another approach avoiding parametric assumptions and unlike a mixture of parametric densities, are less impeded by uncertainty about the appropriate number of sub-groups (Dey et al., 1999; Teh et al., 2006; Teh, 2010). The DPP method deals with possible clustering in the data without trying to specify the number of clusters, except perhaps a maximum conceivable number. Let c02-math-1119 be drawn from a distribution with unknown parameters c02-math-1120, where a Dirichlet process prior is adopted for the c02-math-1121, but a conventional parametric prior for the c02-math-1122. The Dirichlet process involves a random distribution c02-math-1123 centred on a baseline prior c02-math-1124 from which candidate values for c02-math-1125 are drawn, and precision parameter describing the concentration ...

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