Cornuet J M, Beaumont M A
Centre de Biologie et de Gestion des Populations, Institut National de la Recherche Agronomique, Campus International de Baillarguet, CS 30016 Montferrier-sur-Lez, 34988 Saint-Gély-du-Fesc Cedex, France.
Theor Popul Biol. 2007 Feb;71(1):12-9. doi: 10.1016/j.tpb.2006.06.004. Epub 2006 Jun 15.
Stephens and Donnelly have introduced a simple yet powerful importance sampling scheme for computing the likelihood in population genetic models. Fundamental to the method is an approximation to the conditional probability of the allelic type of an additional gene, given those currently in the sample. As noted by Li and Stephens, the product of these conditional probabilities for a sequence of draws that gives the frequency of allelic types in a sample is an approximation to the likelihood, and can be used directly in inference. The aim of this note is to demonstrate the high level of accuracy of "product of approximate conditionals" (PAC) likelihood when used with microsatellite data. Results obtained on simulated microsatellite data show that this strategy leads to a negligible bias over a wide range of the scaled mutation parameter theta. Furthermore, the sampling variance of likelihood estimates as well as the computation time are lower than that obtained with importance sampling on the whole range of theta. It follows that this approach represents an efficient substitute to IS algorithms in computer intensive (e.g. MCMC) inference methods in population genetics.
斯蒂芬斯和唐纳利引入了一种简单却强大的重要性抽样方案，用于计算群体遗传模型中的似然性。该方法的基础是对给定样本中现有等位基因类型的情况下，另一个基因的等位基因类型的条件概率进行近似。正如李和斯蒂芬斯所指出的，对于给出样本中等位基因类型频率的一系列抽样，这些条件概率的乘积是似然性的一种近似，并且可以直接用于推断。本笔记的目的是证明“近似条件概率的乘积”（PAC）似然性在用于微卫星数据时具有高度准确性。在模拟微卫星数据上获得的结果表明，在广泛的尺度突变参数θ范围内，这种策略导致的偏差可以忽略不计。此外，似然性估计的抽样方差以及计算时间都低于在整个θ范围内使用重要性抽样所获得的结果。因此，在群体遗传学中计算机密集型（例如MCMC）推断方法中，这种方法是重要性抽样算法的一种有效替代方法。
