EXACT SIMULATION OF THE WRIGHT-FISHER DIFFUSION
EXACT SIMULATION OF THE WRIGHT-FISHER DIFFUSION
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DOI：
10.1214/16-aap1236
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发表时间：
2017-06-01
影响因子：
1.8
通讯作者：
Spano, Dario
中科院分区：
文献类型：
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作者：
Jenkins, Paul A.;Spano, Dario
Wright-Fisher扩散过程族是一类被广泛使用的进化模型。然而，由于其过渡函数没有已知的封闭形式公式，模拟是困难的。在这篇文章中，我们证明了实际上可以从广泛的Wright-Fisher扩散过程及其桥精确地模拟。对于那些与可逆中性演化相对应的扩散，我们的关键思想是利用过渡函数的特征函数展开；这种方法甚至适用于它的无限维模拟，弗莱明-维奥过程。然后，我们利用回顾性模拟的思想，为具有更一般漂移函数的过程开发了精确的拒绝算法，包括那些建模自然选择的过程。我们的方法也产生了Wright-Fisher扩散矩对偶的精确模拟方法，这是无限叶Kingman聚结树的祖先过程。我们相信我们对扩散模拟的新观点对其他承认转移特征函数展开的模型有希望。
The Wright-Fisher family of diffusion processes is a widely used class of evolutionary models. However, simulation is difficult because there is no known closed-form formula for its transition function. In this article, we demonstrate that it is in fact possible to simulate exactly from a broad class of Wright-Fisher diffusion processes and their bridges. For those diffusions corresponding to reversible, neutral evolution, our key idea is to exploit an eigenfunction expansion of the transition function; this approach even applies to its infinite-dimensional analogue, the Fleming-Viot process. We then develop an exact rejection algorithm for processes with more general drift functions, including those modelling natural selection, using ideas from retrospective simulation. Our approach also yields methods for exact simulation of the moment dual of the Wright-Fisher diffusion, the ancestral process of an infinite-leaf Kingman coalescent tree. We believe our new perspective on diffusion simulation holds promise for other models admitting a transition eigenfunction expansion.