Experiments with the Site Frequency Spectrum |
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Authors: | Raazesh Sainudiin Kevin Thornton Jennifer Harlow James Booth Michael Stillman Ruriko Yoshida Robert Griffiths Gil McVean Peter Donnelly |
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Institution: | Biomathematics Research Centre, Christchurch, New Zealand. r.sainudiin@math.canterbury.ac.nz |
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Abstract: | Evaluating the likelihood function of parameters in highly-structured population genetic models from extant deoxyribonucleic
acid (DNA) sequences is computationally prohibitive. In such cases, one may approximately infer the parameters from summary
statistics of the data such as the site-frequency-spectrum (SFS) or its linear combinations. Such methods are known as approximate
likelihood or Bayesian computations. Using a controlled lumped Markov chain and computational commutative algebraic methods,
we compute the exact likelihood of the SFS and many classical linear combinations of it at a non-recombining locus that is
neutrally evolving under the infinitely-many-sites mutation model. Using a partially ordered graph of coalescent experiments
around the SFS, we provide a decision-theoretic framework for approximate sufficiency. We also extend a family of classical
hypothesis tests of standard neutrality at a non-recombining locus based on the SFS to a more powerful version that conditions
on the topological information provided by the SFS. |
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