Inference and rare event simulation for stopped Markov processes via reverse-time sequential Monte Carlo

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 Naga...

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Bibliographic Details
Published in:Statistics and computing 2018, Vol.28 (1), p.131-144
Main Authors: Koskela, Jere, Spanò, Dario, Jenkins, Paul A.
Format: Article
Language:English
Subjects:
Adaptive algorithms
Artificial Intelligence
Computer simulation
Conditioning
Epidemics
Markov analysis
Markov chains
Mathematics and Statistics
Monte Carlo simulation
Multilevel
Probability and Statistics in Computer Science
Proposals
Queues
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
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Summary: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.
ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-017-9722-1