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On the local geometry of mixture models

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  • Paul Marriott

Abstract

Despite the well-known difficulties of undertaking inference with mixture models, they are frequently used for modelling. These inferential problems arise because the underlying geometry of a mixture family is very complicated. This paper shows that by adding a simplifying assumption, which frequently is natural statistically, the geometric structure is reduced to a much more tractable form. This enables standard inferential techniques to be applied successfully. One result of studying the local geometry is that it unifies the convex and differential geometric theories of mixture models. The techniques proposed are applied to prediction, random effects and measurement error models. Copyright Biometrika Trust 2002, Oxford University Press.

Suggested Citation

  • Paul Marriott, 2002. "On the local geometry of mixture models," Biometrika, Biometrika Trust, vol. 89(1), pages 77-93, March.
    • Handle: RePEc:oup:biomet:v:89:y:2002:i:1:p:77-93
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    Cited by:

    1. Zhiyue Huang & Paul Marriott, 2016. "Parameterizing mixture models with generalized moments," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(2), pages 269-297, April.

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