Markov chain importance sampling with applications to rare event probability estimation
نویسندگان
چکیده
We present a versatile Monte Carlo method for estimating multidimensional integrals, with applications to rare-event probability estimation. The method fuses two distinct and popular Monte Carlo simulation methods — Markov chain Monte Carlo and importance sampling — into a single algorithm. We show that for some illustrative and applied numerical examples the proposed Markov Chain importance sampling algorithm performs better than methods based solely on importance sampling or MCMC.
منابع مشابه
An Efficient Algorithm for Rare-event Probability Estimation, Combinatorial Optimization, and Counting
Although importance sampling is an established and effective sampling and estimation technique, it becomes unstable and unreliable for highdimensional problems. The main reason is that the likelihood ratio in the importance sampling estimator degenerates when the dimension of the problem becomes large. Various remedies to this problem have been suggested, including heuristics such as resampling...
متن کاملAutomated 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...
متن کاملAn algorithm for rare-event probability estimation using the product rule of probability theory
Although importance sampling is an established and effective sampling and estimation technique, it becomes unstable and unreliable for highdimensional problems. The main reason is that the likelihood ratio in the importance sampling estimator degenerates when the dimension of the problem becomes large. Various remedies to this problem have been suggested, including heuristics such as resampling...
متن کاملSplit Sampling: Expectations, Normalisation and Rare Events
In this paper we develop a methodology that we call split sampling methods to estimate high dimensional expectations and rare event probabilities. Split sampling uses an auxiliary variable MCMC simulation and expresses the expectation of interest as an integrated set of rare event probabilities. We derive our estimator from a Rao-Blackwellised estimate of a marginal auxiliary variable distribut...
متن کاملPerformance Analysis Conditioned on Rare Events: an Adaptive Simulation Scheme∗
We consider the problem of simulation-based estimation of performance measures for a Markov chain conditioned on a rare event. The conditional law depends on the solution of a multiplicative Poisson equation. An adaptive scheme for learning the latter is proposed and analyzed. An example motivated by a well known problem in communication networks is given. Applications of the basic scheme to ot...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Statistics and Computing
دوره 23 شماره
صفحات -
تاریخ انتشار 2013