Inference and rare event simulation for stopped Markov processes via reverse-time sequential Monte Carlo
Inference and rare event simulation for stopped Markov processes via reverse-time sequential Monte Carlo
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DOI：
10.1007/s11222-017-9722-1
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发表时间：
2018-01-01
影响因子：
2.2
通讯作者：
Jenkins, Paul A.
中科院分区：
文献类型：
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作者：
Koskela, Jere;Spano, Dario;Jenkins, Paul A.
我们提出了一种用于马尔可夫链轨迹的顺序蒙特卡罗算法，该算法具有逆时构建的建议，这在路径被限制为以稀有集合结束时是有利的。逆时提议分布是通过近似长泽公式中格林函数的比率来构建的。条件参数可用于将这些比率解释为给定其他过程的某些坐标的低维条件采样分布。因此，高维设计SMC方案的难度大大降低。根据经验，我们的方法在三个示例中优于自适应多级分割算法：估计排队模型中的溢出概率、扩散遵循狭窄走廊的概率以及网络上流行病模型中感染的初始位置。
We present a sequential Monte Carlo algorithm for Markov chain trajectories with proposals constructed in reverse time, which is advantageous when paths are conditioned to end in a rare set. The reverse time proposal distribution is constructed by approximating the ratio of Green's functions in Nagasawa's formula. Conditioning arguments can be used to interpret these ratios as low-dimensional conditional sampling distributions of some coordinates of the process given the others. Hence, the difficulty in designing SMC proposals in high dimension is greatly reduced. Empirically, our method outperforms an adaptive multilevel splitting algorithm in three examples: estimating an overflow probability in a queueing model, the probability that a diffusion follows a narrowing corridor, and the initial location of an infection in an epidemic model on a network.