MML estimation of the parameters of the spherical fisher distribution

David L. Dowe, Jonathan J. Oliver, Chris S. Wallace

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    Abstract

    The information-theoretic Minimum Message Length (MML) principle leads to a general invariant Bayesian technique for point estimation. We apply MML to the problem of estimating the concentration parameter, n, of spherical Fisher distributions. (Assuming a uniform prior on the field direction, μ, MML simply returns the Maximum Likelihood estimate for μ.) In earlier work, we dealt with the yon Mises circular case, d = 2. We say something about the general case for arbitrary d ≥ 2 and how to derive the MML estimator, but here we only carry out a complete calculation for the spherical distribution~ with d = 3. Our simulation results show that the MML estimator compares very favourably against the classical methods of Maximum Likelihood and marginal Maximum Likelihood (R.A. Fisher (1953), Schou (1978)). Our simulation results also show that the MML estimator compares quite favourably against alternative Bayesian methods.

    Original languageEnglish
    Title of host publicationAlgorithmic Learning Theory - 7th International Workshop, ALT 1996, Proceedings
    EditorsSetsuo Arikawa, Arun K. Sharma
    PublisherSpringer
    Pages213-227
    Number of pages15
    ISBN (Print)3540618635, 9783540618638
    Publication statusPublished - 1996
    Event7th International Workshop on Algorithmic Learning Theory, ALT 1996 - Sydney, Australia
    Duration: 23 Oct 199625 Oct 1996

    Publication series

    NameLecture Notes in Computer Science
    PublisherSpringer
    Volume1160
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Conference

    Conference7th International Workshop on Algorithmic Learning Theory, ALT 1996
    CountryAustralia
    CitySydney
    Period23/10/9625/10/96

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