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Calculation of marginal densities for parameters of multinomial distributions

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Abstract

The full Bayesian analysis of multinomial data using informative and flexible prior distributions has, in the past, been restricted by the technical problems involved in performing the numerical integrations required to obtain marginal densities for parameters and other functions thereof. In this paper it is shown that Gibbs sampling is suitable for obtaining accurate approximations to marginal densities for a large and flexible family of posterior distributions—the Å family. The method is illustrated with a three-way contingency table. Two alternative Monte Carlo strategies are also discussed.

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Authors and Affiliations

  1. University of Southampton, SO9 5NH, Highfield, Southampton, UK

    Jonathan J. Forster (Faculty of Mathematical Studies)

  2. British Heart Foundation Cardiovascular Statistics Group, Department of Mathematics, University of Nottingham, NG7 2RD, University Park, Nottingham, UK

    Allan M. Skene

Authors
  1. Jonathan J. Forster
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  2. Allan M. Skene
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Forster, J.J., Skene, A.M. Calculation of marginal densities for parameters of multinomial distributions. Stat Comput 4, 279–286 (1994). https://doi.org/10.1007/BF00156751

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