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September 2009 Maximum likelihood estimates under k-allele models with selection can be numerically unstable
Erkan Ozge Buzbas, Paul Joyce
Ann. Appl. Stat. 3(3): 1147-1162 (September 2009). DOI: 10.1214/09-AOAS237


The stationary distribution of allele frequencies under a variety of Wright–Fisher k-allele models with selection and parent independent mutation is well studied. However, the statistical properties of maximum likelihood estimates of parameters under these models are not well understood. Under each of these models there is a point in data space which carries the strongest possible signal for selection, yet, at this point, the likelihood is unbounded. This result remains valid even if all of the mutation parameters are assumed to be known. Therefore, standard simulation approaches used to approximate the sampling distribution of the maximum likelihood estimate produce numerically unstable results in the presence of substantial selection. We describe the Bayesian alternative where the posterior distribution tends to produce more accurate and reliable interval estimates for the selection intensity at a locus.


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Erkan Ozge Buzbas. Paul Joyce. "Maximum likelihood estimates under k-allele models with selection can be numerically unstable." Ann. Appl. Stat. 3 (3) 1147 - 1162, September 2009.


Published: September 2009
First available in Project Euclid: 5 October 2009

zbMATH: 1196.62137
MathSciNet: MR2750390
Digital Object Identifier: 10.1214/09-AOAS237

Keywords: heterozygote advantage , instability , maximum likelihood , multiple allele models , posterior analysis , Selective overdominance

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.3 • No. 3 • September 2009
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