Related papers: Towards zero variance estimators for rare event pr…
Let $(X_n:n\geq 0)$ be a sequence of i.i.d. r.v.'s with negative mean. Set $S_0=0$ and define $S_n=X_1+... +X_n$. We propose an importance sampling algorithm to estimate the tail of $M=\max \{S_n:n\geq 0\}$ that is strongly efficient for…
We give a high precision polynomial-time approximation scheme for the supremum of any honest n-variate (n+2)-nomial with a constant term, allowing real exponents as well as real coefficients. Our complexity bounds count field operations and…
We consider perpetuities of the form D = B_1 exp(Y_1) + B_2 exp(Y_1+Y_2) + ... where the Y_j's and B_j's might be i.i.d. or jointly driven by a suitable Markov chain. We assume that the Y_j's satisfy the so-called Cramer condition with…
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…
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…
Estimating the probability of rare channel conditions is a central challenge in ultra-reliable wireless communication, where random events, such as deep fades, can cause sudden variations in the channel quality. This paper proposes a…
We consider the task of estimating a conditional density using i.i.d. samples from a joint distribution, which is a fundamental problem with applications in both classification and uncertainty quantification for regression. For joint…
Importance sampling is a well developed method in statistics. Given a random variable $X$, the problem of estimating its expected value $\mu$ is addressed. The standard approach is to use the sample mean as an estimator $\bar x$. In…
We present a method for approximating solutions of Stochastic Differential Equations (SDEs) with arbitrary rates. This approximation is derived for bounded and measurable test functions. Specifically, we demonstrate that, leveraging the…
In rare-event simulation, an importance sampling (IS) estimator is regarded as efficient if its relative error, namely the ratio between its standard deviation and mean, is sufficiently controlled. It is widely known that when a rare-event…
We propose a new estimation procedure of the conditional density for independent and identically distributed data. Our procedure aims at using the data to select a function among arbitrary (at most countable) collections of candidates. By…
The Adaptive Multilevel Splitting algorithm is a very powerful and versatile iterative method to estimate the probability of rare events, based on an interacting particle systems. In an other article, in a so-called idealized setting, the…
This paper presents a sharp approximation of the density of long runs of a random walk conditioned on its end value or by an average of a functions of its summands as their number tends to infinity. The conditioning event is of moderate or…
This paper shows that large nonparametric classes of conditional multivariate densities can be approximated in the Kullback--Leibler distance by different specifications of finite mixtures of normal regressions in which normal means and…
Extreme weather events epitomize high cost: to society through their physical impacts, and to computer servers that simulate them to assess risk and advance physical understanding. It costs hundreds of simulation years to sample a few…
Understanding rare events is critical across domains ranging from signal processing to reliability and structural safety, extreme-weather forecasting, and insurance. The analysis of rare events is a computationally challenging problem,…
Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient…
The efficient calculation of rare-event kinetics in complex dynamical systems, such as the rate and pathways of ligand dissociation from a protein, is a generally unsolved problem. Markov state models can systematically integrate ensembles…
We consider the estimation of rare-event probabilities using sample proportions output by naive Monte Carlo or collected data. Unlike using variance reduction techniques, this naive estimator does not have a priori relative efficiency…
We address the estimation of "extreme" conditional quantiles i.e. when their order converges to one as the sample size increases. Conditions on the rate of convergence of their order to one are provided to obtain asymptotically Gaussian…