Related papers: Efficient simulation for dependent rare events wit…
In the linear random effects model, when distributional assumptions such as normality of the error variables cannot be justified, moments may serve as alternatives to describe relevant distributions in neighborhoods of their means.…
In this work we propose an adaptive multilevel version of subset simulation to estimate the probability of rare events for complex physical systems. Given a sequence of nested failure domains of increasing size, the rare event probability…
Rare event simulation and rare event probability estimation are important tasks within the analysis of systems subject to uncertainty and randomness. Simultaneously, accurately estimating rare event probabilities is an inherently difficult…
For rare events described in terms of Markov processes, truly unbiased estimation of the rare event probability generally requires the avoidance of numerical approximations of the Markov process. Recent work in the exact and…
In this work, we propose an algorithm to simulate rare events for electronic circuit design. Our approach heavily relies on a smart use of importance sampling, which enables us to tackle probabilities of the magnitude 10 --10. Not only can…
This paper provides a detailed introductory description of Subset Simulation, an advanced stochastic simulation method for estimation of small probabilities of rare failure events. A simple and intuitive derivation of the method is given…
Rare events play a key role in many applications and numerous algorithms have been proposed for estimating the probability of a rare event. However, relatively little is known on how to quantify the sensitivity of the probability with…
This paper develops a flexible method for decreasing the variance of estimators for complex experiment effect metrics (e.g. ratio metrics) while retaining asymptotic unbiasedness. This method uses the auxiliary information about the…
Sequential estimators are proposed for the relative risk, odds ratio, log relative risk or log odds ratio of a dichotomous attribute in two populations. The estimators take the same number of observations from each population, and guarantee…
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…
We consider systems of stochastic differential equations with multiple scales and small noise and assume that the coefficients of the equations are ergodic and stationary random fields. Our goal is to construct provably-efficient importance…
Extreme value analysis is an essential methodology in the study of rare and extreme events, which hold significant interest in various fields, particularly in the context of environmental sciences. Models that employ the exceedances of…
Extreme values of real phenomena are events that occur with low frequency, but can have a large impact on real life. These are, in many practical problems, high-dimensional by nature (e.g. Tawn, 1990; Coles and Tawn, 1991). To study these…
In public discussions of the quality of forecasts, attention typically focuses on the predictive performance in cases of extreme events. However, the restriction of conventional forecast evaluation methods to subsets of extreme observations…
We analyse the splitting algorithm performance in the estimation of rare event probabilities and this in a discrete multidimensional framework. For this we assume that each threshold is partitioned into disjoint subsets and the probability…
Importance sampling has been known as a powerful tool to reduce the variance of Monte Carlo estimator for rare event simulation. Based on the criterion of minimizing the variance of Monte Carlo estimator within a parametric family, we…
This paper deals with (finite or infinite) sequences of arbitrary independent events in some probability space. We find sharp lower bounds for the probability of a union of such events when the sum of their probabilities is given. The…
We study the extreme events taking place on complex networks. The transport on networks is modelled using random walks and we compute the probability for the occurance and recurrence of extreme events on the network. We show that the nodes…
We approach a class of discrete event simulation-based optimization problems using optimality in probability, an approach which yields what is termed a "champion solution". Compared to the traditional optimality in expectation, this…
Dependency functions of dependent variables are relevant for i) performing uncertainty quantification and sensitivity analysis in presence of dependent variables and/or correlated variables, and ii) simulating random dependent variables. In…