Improved Versions of Common Estimators of the Recombination Rate

Abstract

Abstract

The scaled recombination parameter \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\rho$$ \end{document} is one of the key parameters, turning up frequently in population genetic models. Accurate estimates of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\rho$$ \end{document} are difficult to obtain, as recombination events do not always leave traces in the data. One of the most widely used approaches is composite likelihood. Here, we show that popular implementations of composite likelihood estimators can often be uniformly improved by optimizing the trade-off between bias and variance. The amount of possible improvement depends on parameters such as the sequence length, the sample size, and the mutation rate, and it can be considerable in some cases. It turns out that approximate Bayesian computation, with composite likelihood as a summary statistic, also leads to improved estimates, but now in terms of the posterior risk. Finally, we demonstrate a practical application on real data from Drosophila.