Related papers: Large deviation theory-based adaptive importance s…
Sampling is an important tool for estimating large, complex sums and integrals over high dimensional spaces. For instance, important sampling has been used as an alternative to exact methods for inference in belief networks. Ideally, we…
Driven by applications in telecommunication networks, we explore the simulation task of estimating rare event probabilities for tandem queues in their steady state. Existing literature has recognized that importance sampling methods can be…
To efficiently evaluate system reliability based on Monte Carlo simulation, importance sampling is used widely. The optimal importance sampling density was derived in 1950s for the deterministic simulation model, which maps an input to an…
Importance sampling is a technique that is commonly used to speed up Monte Carlo simulation of rare events. However, little is known regarding the design of efficient importance sampling algorithms in the context of queueing networks. The…
Random geometric graphs defined on Euclidean subspaces, also called Gilbert graphs, are widely used to model spatially embedded networks across various domains. In such graphs, nodes are located at random in Euclidean space, and any two…
Large deviation theory has provided important clues for the choice of importance sampling measures for Monte Carlo evaluation of exceedance probabilities. However, Glasserman and Wang [Ann. Appl. Probab. 7 (1997) 731--746] have given…
The estimation of the probability of rare events is an important task in reliability and risk assessment. We consider failure events that are expressed in terms of a limit state function, which depends on the solution of a partial…
In the field of computational physics and material science, the efficient sampling of rare events occurring at atomic scale is crucial. It aids in understanding mechanisms behind a wide range of important phenomena, including protein…
Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions…
Probability density function estimation with weighted samples is the main foundation of all adaptive importance sampling algorithms. Classically, a target distribution is approximated either by a non-parametric model or within a parametric…
The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic…
The Adaptive Multilevel Splitting (AMS) algorithm is a powerful and versatile method for the simulation of rare events. It is based on an interacting (via a mutation-selection procedure) system of replicas, and depends on two integer…
We propose an adaptive importance sampling scheme for the simulation of rare events when the underlying dynamics is given by a diffusion. The scheme is based on a Gibbs variational principle that is used to determine the optimal (i.e.…
Importance sampling (IS) is a widely used simulation method for estimating rare event probabilities. In IS, the relative variance of an estimator is the most common measure of estimator accuracy, and the focus of existing literature is on…
The basic idea of importance sampling is to use independent samples from a proposal measure in order to approximate expectations with respect to a target measure. It is key to understand how many samples are required in order to guarantee…
We propose a class of strongly efficient rare event simulation estimators for random walks and compound Poisson processes with a regularly varying increment/jump-size distribution in a general large deviations regime. Our estimator is based…
We present an algorithm for finding the probabilities of rare events in nonequilibrium processes. The algorithm consists of evolving the system with a modified dynamics for which the required event occurs more frequently. By keeping track…
Entropy estimation is of practical importance in information theory and statistical science. Many existing entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for…
In this paper, we propose an efficient importance sampling algorithm for rare event simulation under copula models. In the algorithm, the derived optimal probability measure is based on the criterion of minimizing the variance of the…
Importance sampling is a popular method for efficient computation of various properties of a distribution such as probabilities, expectations, quantiles etc. The output of an importance sampling algorithm can be represented as a weighted…