DISAT and Center for Computational Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy and Collegio Carlo Alberto, Via Real Collegio 30, 10024 Moncalieri, Italy.
DISAT and Center for Computational Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy and Collegio Carlo Alberto, Via Real Collegio 30, 10024 Moncalieri, Italy and Human Genetics Foundation, Via Nizza 52, 10126 Torino, Italy.
Phys Rev Lett. 2014 Mar 21;112(11):118701. doi: 10.1103/PhysRevLett.112.118701. Epub 2014 Mar 17.
We study several Bayesian inference problems for irreversible stochastic epidemic models on networks from a statistical physics viewpoint. We derive equations which allow us to accurately compute the posterior distribution of the time evolution of the state of each node given some observations. At difference with most existing methods, we allow very general observation models, including unobserved nodes, state observations made at different or unknown times, and observations of infection times, possibly mixed together. Our method, which is based on the belief propagation algorithm, is efficient, naturally distributed, and exact on trees. As a particular case, we consider the problem of finding the "zero patient" of a susceptible-infected-recovered or susceptible-infected epidemic given a snapshot of the state of the network at a later unknown time. Numerical simulations show that our method outperforms previous ones on both synthetic and real networks, often by a very large margin.
我们从统计物理的角度研究了网络上不可逆随机传染病模型的几个贝叶斯推断问题。我们推导出了一些方程，这些方程允许我们根据一些观测值准确地计算每个节点状态随时间的后验分布。与大多数现有方法不同，我们允许非常一般的观测模型，包括未观测到的节点、在不同或未知时间进行的状态观测，以及可能混合在一起的感染时间观测。我们的方法基于信念传播算法，高效、自然分布且在树上是精确的。作为一个特例，我们考虑了在未知的未来时间点获取网络状态快照的情况下，从易感染-感染-恢复或易感染-感染传染病中找到“零患者”的问题。数值模拟表明，我们的方法在合成和真实网络上都优于以前的方法，通常优势非常大。
