Multilevel Splitting for Estimating Rare Event Probabilities
Operations Research
Optimal probabilistic fingerprint codes
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Probability in the Engineering and Informational Sciences
Introduction to Rare Event Simulation
Introduction to Rare Event Simulation
Efficient Monte Carlo simulation via the generalized splitting method
Statistics and Computing
Optimal Watermark Embedding and Detection Strategies Under Limited Detection Resources
IEEE Transactions on Information Theory
On the Concentration Properties of Interacting Particle Processes
Foundations and Trends® in Machine Learning
Self-Avoiding Random Dynamics on Integer Complex Systems
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special Issue on Monte Carlo Methods in Statistics
Importance splitting for statistical model checking rare properties
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
On the use of a class of interior point algorithms in stochastic structural optimization
Computers and Structures
Bayesian parameter inference for partially observed stopped processes
Statistics and Computing
| Hi-index | 0.00 |
This paper discusses a novel strategy for simulating rare events and an associated Monte Carlo estimation of tail probabilities. Our method uses a system of interacting particles and exploits a Feynman-Kac representation of that system to analyze their fluctuations. Our precise analysis of the variance of a standard multilevel splitting algorithm reveals an opportunity for improvement. This leads to a novel method that relies on adaptive levels and produces, in the limit of an idealized version of the algorithm, estimates with optimal variance. The motivation for this theoretical work comes from problems occurring in watermarking and fingerprinting of digital contents, which represents a new field of applications of rare event simulation techniques. Some numerical results show performance close to the idealized version of our technique for these practical applications.