Related papers: Multilevel Sequential Importance Sampling for Rare…
This paper proposes a new pathwise sensitivity estimator for chaotic SDEs. By introducing a spring term between the original and perturbated SDEs, we derive a new estimator by importance sampling. The variance of the new estimator increases…
The problem of studying rare events is central to many areas of computer simulations. In a recent paper [Kang, P., et al., Nat. Comput. Sci. 4, 451-460, 2024], we have shown that a powerful way of solving this problem passes through the…
We propose and analyze a method for computing failure probabilities of systems modeled as numerical deterministic models (e.g., PDEs) with uncertain input data. A failure occurs when a functional of the solution to the model is below (or…
Computation of extreme quantiles and tail-based risk measures using standard Monte Carlo simulation can be inefficient. A method to speed up computations is provided by importance sampling. We show that importance sampling algorithms,…
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…
We propose a deep importance sampling method that is suitable for estimating rare event probabilities in high-dimensional problems. We approximate the optimal importance distribution in a general importance sampling problem as the…
Molecular motors and other complex nonequilibrium systems are controlled by large sets of design parameters, and optimizing those parameters requires computing sensitivities -- derivatives of dynamical observables with respect to the…
We develop a theoretical framework for studying numerical estimation of lower previsions, generally applicable to two-level Monte Carlo methods, importance sampling methods, and a wide range of other sampling methods one might devise. We…
Resilience is becoming crucial for future wireless networks, which must withstand, adapt to, and recover from rare but potentially cascading disruptions. This paper develops a sequential Monte Carlo (SMC) simulation framework for such…
In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…
Accurate estimates of long-term risk probabilities and their gradients are critical for many stochastic safe control methods. However, computing such risk probabilities in real-time and in unseen or changing environments is challenging.…
We present a new method for sampling rare and large fluctuations in a non-equilibrium system governed by a stochastic partial differential equation (SPDE) with additive forcing. To this end, we deploy the so-called instanton formalism that…
The multilevel Monte Carlo (MLMC) method for continuous-time Markov chains, first introduced by Anderson and Higham (SIAM Multiscal Model. Simul. 10(1), 2012), is a highly efficient simulation technique that can be used to estimate various…
We propose a new method for estimating rare event probabilities when independent samples are available. It is assumed that the underlying probability measures satisfy a large deviations principle with a scaling parameter $\varepsilon$ that…
We consider the general problem of estimating probabilities which arise as a union of dependent events. We propose a flexible series of estimators for such probabilities, and describe variance reduction schemes applied to the proposed…
Estimating the probability of failure is a critical step in developing safety-critical autonomous systems. Direct estimation methods such as Monte Carlo sampling are often impractical due to the rarity of failures in these systems. Existing…
We consider importance sampling to estimate the probability $\mu$ of a union of $J$ rare events $H_j$ defined by a random variable $\boldsymbol{x}$. The sampler we study has been used in spatial statistics, genomics and combinatorics going…
McKean-Vlasov stochastic differential equations (MVSDEs) describe systems whose dynamics depend on both individual states and the population distribution, and they arise widely in neuroscience, finance, and epidemiology. In many…
Partial differential equation is a powerful tool to characterize various physics systems. In practice, measurement errors are often present and probability models are employed to account for such uncertainties. In this paper, we present a…
Stochastic Differential Equations (SDEs) are used as statistical models in many disciplines. However, intractable likelihood functions for SDEs make inference challenging, and we need to resort to simulation-based techniques to estimate and…