ABC likelihood-free methods for model choice in Gibbs random fields
ABC likelihood-free methods for model choice in Gibbs random fields
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DOI：
10.1214/09-ba412
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发表时间：
2009-01-01
影响因子：
4.4
通讯作者：
Taly, Jean-Francois
中科院分区：
文献类型：
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作者：
Grelaud, Aude;Robert, Christian P.;Taly, Jean-Francois
吉布斯随机场（GRF）是多态统计模型，可用于分析不同类型的依赖，特别是空间相关的数据。然而，当这些模型面临的挑战，选择一个依赖结构，从许多，标准的模型选择方法的使用受到阻碍的吉布斯似然的归一化常数的不可用。特别是，从贝叶斯的角度来看，竞争下的模型的后验概率的计算需要特殊的似然自由模拟技术，如近似贝叶斯计算（ABC）算法，这是广泛使用的群体遗传学。在本文中，我们将展示如何实现ABC算法面向模型选择的吉布斯随机场的一般设置，特别是证明，存在一个足够的统计模型。通过对模型的分布进行重要性抽样，可以进一步提高后验概率的近似精度。该方法的实际方面详细通过两个应用程序，一个iid伯努利模型与一阶马尔可夫链的测试，和两种蛋白质的折叠结构的选择。
Gibbs random fields (GRF) are polymorphous statistical models that can be used to analyse different types of dependence, in particular for spatially correlated data. However, when those models are faced with the challenge of selecting a dependence structure from many, the use of standard model choice methods is hampered by the unavailability of the normalising constant in the Gibbs likelihood. In particular, from a Bayesian perspective, the computation of the posterior probabilities of the models under competition requires special likelihood-free simulation techniques like the Approximate Bayesian Computation (ABC) algorithm that is intensively used in population genetics. We show in this paper how to implement an ABC algorithm geared towards model choice in the general setting of Gibbs random fields, demonstrating in particular that there exists a sufficient statistic across models. The accuracy of the approximation to the posterior probabilities can be further improved by importance sampling on the distribution of the models. The practical aspects of the method are detailed through two applications, the test of an iid Bernoulli model versus a first-order Markov chain, and the choice of a folding structure for two proteins.