Approximating zero-variance importance sampling in a reliability setting

Approximating zero-variance importance sampling in a reliability setting

We consider a class of Markov chain models that includes the highly reliable Markovian systems (HRMS) often used to represent the evolution of multicomponent systems in reliability settings. We are interested in the design of efficient importance sampling (IS) schemes to estimate the reliability of such systems by simulation. For these models, there is in fact a zero-variance IS scheme that can...

Some Advances in Importance Sampling of Reliability Models Based on Zero Variance Approximation

We are interested in estimating, through simulation, the probability of entering a rare failure state before a regeneration state. Since this probability is typically small, we apply importance sampling. The method that we use is based on finding the most likely paths to failure. We present an algorithm that is guaranteed to produce an estimator that meets the conditions presented in [10] [9] f...

Zero-Variance Importance Sampling Estimators for Markov Process Expectations

We study the structure of zero-variance importance sampling estimators for expectations of functionals of Markov processes. For a class of expectations that can be characterized as solutions to linear systems, we show that a zerovariance estimator can be constructed by using an importance distribution that preserves the Markovian nature of the underlying process. This suggests that good practic...

Automated State-Dependent Importance Sampling for Markov Jump Processes via Sampling from the Zero-Variance Distribution

Many complex systems can be modeled via Markov jump processes. Applications include chemical reactions, population dynamics, and telecommunication networks. Rare-event estimation for such models can be difficult and is often computationally expensive, because typically many (or very long) paths of the Markov jump process need to be simulated in order to observe the rare event. We present a stat...

Zero Variance Importance Sampling Driven Potential Tracing Algorithm for Global Illumination