An efficient method for Bayesian model selection is presented for a broad class of continuous-time Markov chain models and is subsequently applied to two important problems in epidemiology. The first problem is to identify the shape of the infectious period distribution; the second problem is to determine whether individuals display symptoms before, at the same time, or after they become infectious. In both cases we show that the correct model can be identified, in the majority of cases, from symptom onset data generated from multiple outbreaks in small populations. The method works by evaluating the likelihood using a particle filter that incorporates a novel importance sampling algorithm designed for partially-observed continuous-time Markov chains. This is combined with another importance sampling method to unbiasedly estimate the model evidence. These come with estimates of precision, which allow for stopping criterion to be employed. Our method is general and can be applied to a wide range of model selection problems in biological and epidemiological systems with intractable likelihood functions.

中文翻译：

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部分观测的流行病模型的贝叶斯模型判别。

针对广泛的连续时间马尔可夫链模型，提出了一种有效的贝叶斯模型选择方法，随后将其应用于流行病学中的两个重要问题。第一个问题是确定传染期分布的形状。第二个问题是确定个体在感染之前，同时或之后是否表现出症状。在这两种情况下，我们都表明，在大多数情况下，可以从少量人群多次暴发产生的症状发作数据中识别出正确的模型。该方法通过使用粒子滤波器评估似然性来工作，该粒子滤波器结合了专为部分观测的连续时间马尔可夫链而设计的新型重要性采样算法。这与另一种重要性抽样方法相结合，可以无偏估计模型证据。这些带有精度估计，这允许采用停止标准。我们的方法是通用的，可以应用于具有难以解决的似然函数的生物学和流行病学系统中的各种模型选择问题。