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arXiv 1601.04096stat.ME
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近似贝叶斯计算的拟合优度统计量

Goodness-of-fit statistics for approximate Bayesian computation

Louisiane Lemaire, Flora Jay, I-Hung Lee, Katalin Csilléry, Michael G. B. Blum

摘要:

近似贝叶斯计算是一种统计框架,它使用数值模拟来校准和比较模型。近似贝叶斯计算依赖于数值模拟,而不是计算似然函数,这使得它适用于生态学和进化中的复杂模型。与统计建模一样,评估拟合优度是近似贝叶斯计算的基本步骤。在这里,我们介绍了一种基于假设检验的拟合优度方法。我们引入了两个检验统计量的基础上的平均距离之间的数值汇总的数据和模拟的。一个检验统计量依赖于用先验预测分布模拟的汇总,而另一个依赖于后验预测分布的模拟。对于不同的聚结模型,我们发现,统计校准良好,这意味着第一类错误可以控制。然而,两种统计量的统计功效在20%至100%的模型中变化极大。在人口推断模型中,这两种统计数据之间的功效差异可以忽略不计,但在一个额外的纯统计示例中,差异很大。在分析重新排序数据以评估人类人口模型时,这两个统计数据证实,亚洲和欧洲数据不能排除非洲以外的瓶颈。我们还考虑了两种形态的蝴蝶物种复杂的背景下模型。一个拟合优度统计量表明两个模型的拟合差,使用后验预测检查确定了导致拟合差的数值总结。拟合优度的统计检验应促进近似贝叶斯计算中模型拟合的评估。基于先验预测分布模拟的检验统计量在R abc包的gfit函数中实现。

英文摘要:

Approximate Bayesian computation is a statistical framework that uses numerical simulations to calibrate and compare models. Instead of computing likelihood functions, Approximate Bayesian computation relies on numerical simulations, which makes it applicable to complex models in ecology and evolution. As usual for statistical modeling, evaluating goodness-of-fit is a fundamental step for Approximate Bayesian Computation. Here, we introduce a goodness-of-fit approach based on hypothesis-testing. We introduce two test statistics based on the mean distance between numerical summaries of the data and simulated ones. One test statistic relies on summaries simulated with the prior predictive distribution whereas the other one relies on simulations from the posterior predictive distribution. For different coalescent models, we find that the statistics are well calibrated, meaning that the type I error can be controlled. However, the statistical power of the two statistics is extremely variable across models ranging from 20% to 100%. The difference of power between the two statistics is negligible in models of demographic inference but substantial in an additional and purely statistical example. When analyzing resequencing data to evaluate models of human demography, the two statistics confirm that an out-of-Africa bottleneck cannot be rejected for Asiatic and European data. We also consider two speciation models in the context of a butterfly species complex. One goodness-of-fit statistic indicates a poor fit for both models, and the numerical summaries causing the poor fit were identified using posterior predictive checks. Statistical tests for goodness-of-fit should foster evaluation of model fit in Approximate Bayesian Computation. The test statistic based on simulations from the prior predictive distribution is implemented in the gfit function of the R abc package.

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