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Biometrika 2002 89(1):77-93; doi:10.1093/biomet/89.1.77
© 2002 by Biometrika Trust
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On the local geometry of mixture models

Paul Marriott1

1 Department of Statistics & Applied Probability, National University of Singapore, 3 Science Drive 2, Singapore 117543 stapkm{at}nus.edu.sg

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.

Key Words: Convex geometry; Differential geometry; Measurement error; Mixture model; Prediction; Random effects model; Statistical manifold

Received June 2000. Revised July 2001


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