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Likelihood ratios for the infinite alleles model

Part of: Parametric inference Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Paul Joyce
Paul Joyce*
Affiliation:
University of Idaho
*
∗ Postal address: University of Idaho, Department of Mathematics and Statistics, Moscow, Idaho 83843, USA.
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Abstract

The stationary distribution for the population frequencies under an infinite alleles model is described as a random sequence (x1, x2, · ··) such that Σxi = 1. Likelihood ratio theory is developed for random samples drawn from such populations. As a result of the theory, it is shown that any parameter distinguishing an infinite alleles model with selection from the neutral infinite alleles model cannot be consistently estimated based on gene frequencies at a single locus. Furthermore, the likelihood ratio (neutral versus selection) converges to a non-trivial random variable under both hypotheses. This shows that if one wishes to test a completely specified infinite alleles model with selection against neutrality, the test will not obtain power 1 in the limit.

Keywords

EXCHANGEABLE EQUIVALENCE RELATIONSMARTINGALES

MSC classification

Primary: 62F05: Asymptotic properties of tests
Secondary: 60G42: Martingales with discrete parameter
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 3 , September 1994 , pp. 595 - 605
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

This research is supported by National Science Foundation grant DMS 92-07410.

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