Related papers: Efficient Rare-Event Simulation for Multiple Jump …
The EM algorithm is a powerful tool for maximum likelihood estimation with missing data. In practice, the calculations required for the EM algorithm are often intractable. We review numerous methods to circumvent this intractability, all of…
Rare weather and climate events, such as heat waves and floods, can bring tremendous social costs. Climate data is often limited in duration and spatial coverage, and climate forecasting has often turned to simulations of climate models to…
Adaptive importance sampling is a class of techniques for finding good proposal distributions for importance sampling. Often the proposal distributions are standard probability distributions whose parameters are adapted based on the…
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…
We develop a novel procedure for estimating the optimizer of general convex stochastic optimization problems of the form $\min_{x\in\mathcal{X}} \mathbb{E}[F(x,\xi)]$, when the given data is a finite independent sample selected according to…
A fast algorithm for path sampling in path integral Monte Carlo simulations is proposed. The algorithm utilizes the Levy-Ciesielski implementation of Lie-Trotter products to achieve a mathematically proven computational cost of n*log_2(n)…
Given a sample from a discretely observed L\'evy process $X=(X_t)_{t\geq 0}$ of the finite jump activity, the problem of nonparametric estimation of the L\'evy density $\rho$ corresponding to the process $X$ is studied. An estimator of…
We suggest a general framework for simulation of the triplet $(X_T,\bar X_ T,\tau_T)$ (L\'evy process, its extremum, and hitting time of the extremum), and, separately, $X_T,\bar X_ T$ and pairs $(X_T,\bar X_ T)$, $(\bar X_ T,\tau_T)$,…
We present three algorithms for calculating rate constants and sampling transition paths for rare events in simulations with stochastic dynamics. The methods do not require a priori knowledge of the phase space density and are suitable for…
We characterize the complex, heavy-tailed probability distribution functions (pdf) describing the response and its local extrema for structural systems subjected to random forcing that includes extreme events. Our approach is based on the…
This work addresses the estimation of rare-event quantities expressed as expectations of smooth observables of solutions to a broad class of McKean--Vlasov stochastic differential equations (MV-SDEs). Building on the double loop Monte Carlo…
Modern statistical analyses often encounter datasets with massive sizes and heavy-tailed distributions. For datasets with massive sizes, traditional estimation methods can hardly be used to estimate the extreme value index directly. To…
We provide a novel expression of the scale function for a L\'evy processes with negative phase-type jumps. It is in terms of a certain transition rate matrix which is explicit up to a single positive number. A monotone iterative scheme for…
We explore efficient estimation of statistical quantities, particularly rare event probabilities, for stochastic reaction networks. Consequently, we propose an importance sampling (IS) approach to improve the Monte Carlo (MC) estimator…
Learning-based methodologies increasingly find applications in safety-critical domains like autonomous driving and medical robotics. Due to the rare nature of dangerous events, real-world testing is prohibitively expensive and unscalable.…
Exploiting stochastic path integral theory, we obtain \emph{by simulation} substantial gains in efficiency for the computation of reaction rates in one-dimensional, bistable, overdamped stochastic systems. Using a well-defined measure of…
The Reversible Jump algorithm is one of the most widely used Markov chain Monte Carlo algorithms for Bayesian estimation and model selection. A generalized multiple-try version of this algorithm is proposed. The algorithm is based on…
Parameter estimation for discretely observed Markov processes is a challenging problem. However, simulation of Markov processes is straightforward using the Gillespie algorithm. We exploit this ease of simulation to develop an effective…
We obtain general lower estimates of transition densities of jump L\'evy processes. We use them for processes with L\'evy measures having bounded support, processes with exponentially decaying L\'evy measures for large times and for…
Threshold selection plays a key role for various aspects of statistical inference of rare events. Most classical approaches tackling this problem for heavy-tailed distributions crucially depend on tuning parameters or critical values to be…