On optimality of kernels for approximate Bayesian computation using sequential Monte Carlo.
On optimality of kernels for approximate Bayesian computation using sequential Monte Carlo.
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DOI：
10.1515/sagmb-2012-0069
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发表时间：
2013-03-26
影响因子：
0.9
通讯作者：
Stumpf, Michael P H
中科院分区：
文献类型：
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作者：
Filippi, Sarah;Barnes, Chris P;Stumpf, Michael P H
在过去的几年中，近似贝叶斯计算（ABC）在分析群体遗传学、流行病学和系统生物学中出现的复杂模型方面越来越受欢迎。序贯蒙特卡罗（SMC）方法已成为ABC中的工作马匹。在这里，我们将讨论如何构建扰动核所需的ABC SMC方法，以构建一个序列的分布，从一个适当定义的先验和收敛到未知的后验。我们推导出不同的内核，这是基于分布和扰动粒子的分布之间的Kullback-Leibler分歧的最优性准则。我们将证明，对于许多复杂的后验分布，局部自适应内核往往表现出最好的性能。我们发现，增加适度的成本，适应核函数很容易重新获得较高的接受率。我们展示了一系列玩具的例子，说明了ABC在现实世界中的应用所面临的一些挑战的计算效率的提高，然后转向两个苛刻的参数推断问题，在分子生物学，突出了巨大的提高效率，可以从选择最佳内核。最后，我们一般讨论的合理选择扰动核在ABC SMC设置。
Approximate Bayesian computation (ABC) has gained popularity over the past few years for the analysis of complex models arising in population genetics, epidemiology and system biology. Sequential Monte Carlo (SMC) approaches have become work-horses in ABC. Here we discuss how to construct the perturbation kernels that are required in ABC SMC approaches, in order to construct a sequence of distributions that start out from a suitably defined prior and converge towards the unknown posterior. We derive optimality criteria for different kernels, which are based on the Kullback-Leibler divergence between a distribution and the distribution of the perturbed particles. We will show that for many complicated posterior distributions, locally adapted kernels tend to show the best performance. We find that the added moderate cost of adapting kernel functions is easily regained in terms of the higher acceptance rate. We demonstrate the computational efficiency gains in a range of toy examples which illustrate some of the challenges faced in real-world applications of ABC, before turning to two demanding parameter inference problems in molecular biology, which highlight the huge increases in efficiency that can be gained from choice of optimal kernels. We conclude with a general discussion of the rational choice of perturbation kernels in ABC SMC settings.