Related papers: Rare event simulation for electronic circuit desig…
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…
Atypical, rare trajectories of dynamical systems are important: they are often the paths for chemical reactions, the haven of (relative) stability of planetary systems, the rogue waves that are detected in oil platforms, the structures that…
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…
An important step in the design of autonomous systems is to evaluate the probability that a failure will occur. In safety-critical domains, the failure probability is extremely small so that the evaluation of a policy through Monte Carlo…
Estimating the probability of failures or accidents with aerospace systems is often necessary when new concepts or designs are introduced, as it is being done for Autonomous Aircraft. If the design is safe, as it is supposed to be, accident…
We describe a practical approach for accessing the logical failure rates of quantum error-correcting (QEC) circuits under low physical (component) failure rate regimes. Standard Monte Carlo is often the de facto approach for studying the…
This article focuses, in the context of epidemic models, on rare events that may possibly correspond to crisis situations from the perspective of Public Health. In general, no close analytic form for their occurrence probabilities is…
In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable $V$ satisfying the distributional equation $V\stackrel{\mathcal{D}}{=}f(V)$,…
In this paper we use splitting technique to estimate the probability of hitting a rare but critical set by the continuous component of a switching diffusion. Instead of following classical approach we use Wonham filter to achieve multiple…
We consider the problem of choosing design parameters to minimize the probability of an undesired rare event that is described through the average of $n$ iid random variables. Since the probability of interest for near optimal design…
The estimation of rare event or failure probabilities in high dimensions is of interest in many areas of science and technology. We consider problems where the rare event is expressed in terms of a computationally costly numerical model.…
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…
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…
In this paper we study rare events associated to solutions of elliptic partial differential equations with spatially varying random coefficients. The random coefficients follow the lognormal distribution, which is determined by a Gaussian…
Particle splitting methods are considered for the estimation of rare events. The probability of interest is that a Markov process first enters a set $B$ before another set $A$, and it is assumed that this probability satisfies a large…
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…
For the validation of safety-critical systems regarding safety and comfort, e.g., in the context of automated driving, engineers often have to cope with large (parametric) test spaces for which it is infeasible to test through all possible…
We develop a new algorithm for the estimation of rare event probabilities associated with the steady-state of a Markov stochastic process with continuous state space $\mathbb R^d$ and discrete time steps (i.e. a discrete-time $\mathbb…
We explore past and recent developments in rare-event probability estimation with a particular focus on a novel Monte Carlo technique Empirical Likelihood Maximization (ELM). This is a versatile method that involves sampling from a sequence…
A computer code can simulate a system's propagation of variation from random inputs to output measures of quality. Our aim here is to estimate a critical output tail probability or quantile without a large Monte Carlo experiment. Instead,…