Bayesian Inference of Epidemics on Networks via Belief Propagation
Bayesian Inference of Epidemics on Networks via Belief Propagation
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DOI：
10.1103/physrevlett.112.118701
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发表时间：
2014-03-17
影响因子：
8.6
通讯作者：
Zecchina, Riccardo
中科院分区：
文献类型：
--
作者：
Altarelli, Fabrizio;Braunstein, Alfredo;Zecchina, Riccardo
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贝叶斯推断问题。我们推导方程，使我们能够准确地计算后验分布的时间演化的每个节点的状态给出一些意见。与大多数现有方法不同，我们允许非常一般的观测模型，包括未观测的节点，在不同或未知时间进行的状态观测，以及感染时间的观测，可能混合在一起。我们的方法，这是基于信念传播算法，是有效的，自然分布，和准确的树上。作为一个特殊的情况下，我们考虑的问题，找到“零病人”的一个不确定的感染-恢复或不确定的感染流行病的网络状态的快照在稍后的未知时间。数值模拟表明，我们的方法优于以前的合成和真实的网络，往往是一个非常大的保证金。
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.