Conjugate Bayes discrimination with infinitely many variables. (English) Zbl 0745.62061
Summary: The problem considered is that of discrimination between two multivariate normal populations, with common dispersion structure, when the number of variables that can be observed is unlimited. We consider a Bayesian analysis, using a natural conjugate prior for the normal distribution parameters. One implication of this is that, with prior probability 1, the parameters will be such as to allow asymptotically perfect discrimination between the populations. We also find conditions under which this perfect discrimination will be possible, even in the absence of knowledge of the parameter values.
MSC:
| 62H30 | Classification and discrimination; cluster analysis (statistical aspects) |
| 62C10 | Bayesian problems; characterization of Bayes procedures |
Keywords:
multivariate normal populations; common dispersion structure; natural conjugate prior; asymptotically perfect discriminationReferences:
| [1] | Dawid, A. P., Conditional independence in statistical theory (with discussion), J. Roy. Statist. Soc. Ser. B, 41, 1-31 (1979) · Zbl 0408.62004 |
| [2] | Dawid, A. P., Some matrix-variate distribution theory: Notational considerations and a Bayesian application, Biometrika, 68, 265-274 (1981) · Zbl 0464.62039 |
| [3] | Dawid, A. P., The infinite regress and its conjugate analysis (with discussion), (Bernardo, J. M.; DeGroot, M. H.; Lindley, D. V.; Smith, A. F.M, Bayesian Statistics 3 (1988), Oxford Univ. Press: Oxford Univ. Press Oxford/New York), 95-110 · Zbl 0706.62031 |
| [4] | Dickey, J. M., Matricvariate generalizations of the multivariate \(t\) distribution and the inverted multivariate \(t\) distribution, Ann. Math. Statist., 38, 511-518 (1967) · Zbl 0158.18403 |
| [5] | Geisser, S., Posterior odds for multivariate normal classifications, J. Roy. Statist. Soc. Ser. B, 25, 368-376 (1964) · Zbl 0126.34302 |
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