MURRAY AITKIN, University of Melbourne
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This talk discusses a set of astronomical data on recession velocities of galaxies,
presented by Roeder in JASA 1990. The data show three well-separated clusters,
and the question of interest is how many components are present in a Gaussian
mixture.
Published Bayesian analyses vary widely in their answers to this question. We give
another Bayesian analysis based on the posterior distributions of the likelihoods
(Aitkin 2001, 2010, 2011) for each number of components. This comes to a
reasonable conclusion, which does not depend on the priors for the models'
parameters.
References
Aitkin, M. (2001) Likelihood and Bayesian analysis of mixtures. Statistical Modelling
1, 287-304.
Aitkin, M. (2010) Statistical Inference: an Integrated Bayesian/Likelihood Approach.
Chapman and Hall.
Aitkin, M. (2011) How many components in a finite mixture? in Mixtures: Estimation
and Applications, eds K.L.Mengersen, C.P. Robert and D.M. Titterington, pp. 277-292.
Wiley.
Roeder, K. (1990) Density estimation with confidence sets exemplified by superclusters
and voids in the galaxies. JASA 85, 617-624.