Exact filtering for partially observed continuous time models
Exact filtering for partially observed continuous time models
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DOI：
10.1111/j.1467-9868.2004.05561.x
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发表时间：
2004-01-01
影响因子：
5.8
通讯作者：
Meligkotsidou, L
中科院分区：
文献类型：
--
作者：
Fearnhead, P;Meligkotsidou, L
前后向算法是一种精确的滤波算法，可以有效地计算似然，并可用于从后验分布进行模拟。使用一个简单的结果，涉及伽马随机变量与不同的利率，假发显示如何向前向后算法可以用来计算分布的伽马随机变量的总和，并模拟从他们的联合分布给定他们的总和。一个应用是计算马尔可夫过程中特定事件的时间密度，因为这个时间是指数分布的interevent时间之和。这使我们能够将向前向后算法应用于一系列新问题。我们证明了我们的方法上的三个问题：计算似然和模拟等位基因频率下的非中性群体遗传模型，分析随机流行病模型和模拟物种形成时间在遗传学。
The forward-backward algorithm is an exact filtering algorithm which can efficiently calculate likelihoods, and which can be used to simulate from posterior distributions. Using a simple result which relates gamma random variables with different rates, wig show how the forward-backward algorithm can be used to calculate the distribution of a sum of gamma random variables, and to simulate from their joint distribution given their sum. One application is to calculating the density of the time of a specific event in a Markov process, as this time is the sum of exponentially distributed interevent times. This enables us to apply the forward-backward algorithm to a range of new problems. We demonstrate our method on three problems: calculating likelihoods and simulating allele frequencies under a non-neutral population genetic model, analysing a stochastic epidemic model and simulating speciation times in phylogenetics.