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Padé approximants and exact two-locus sampling distributions
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Jenkins, Paul and Song, Yun S. (2012) Padé approximants and exact two-locus sampling distributions. Annals of Applied Probability, Vol.22 (No.2). pp. 576-607. doi:10.1214/11-AAP780 ISSN 1050-5164.
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Official URL: http://dx.doi.org/10.1214/11-AAP780
Abstract
For population genetics models with recombination, obtaining an exact, analytic sampling distribution has remained a challenging open problem for several decades. Recently, a new perspective based on asymptotic series has been introduced to make progress on this problem. Specifically, closed-form expressions have been derived for the first few terms in an asymptotic expansion of the two-locus sampling distribution when the recombination rate ρ is moderate to large. In this paper, a new computational technique is developed for finding the asymptotic expansion to an arbitrary order. Computation in this new approach can be automated easily. Furthermore, it is proved here that only a finite number of terms in the asymptotic expansion is needed to recover (via the method of Padé approximants) the exact two-locus sampling distribution as an analytic function of ρ; this function is exact for all values of ρ ∈ [0, ∞). It is also shown that the new computational framework presented here is flexible enough to incorporate natural selection.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Journal or Publication Title: | Annals of Applied Probability | ||||
Publisher: | Institute of Mathematical Statistics | ||||
ISSN: | 1050-5164 | ||||
Official Date: | April 2012 | ||||
Dates: |
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Volume: | Vol.22 | ||||
Number: | No.2 | ||||
Page Range: | pp. 576-607 | ||||
DOI: | 10.1214/11-AAP780 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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