Related papers: Efficient rare event estimation for multimodal and…

A rare event is defined by a low probability of occurrence. Accurate estimation of such small probabilities is of utmost importance across diverse domains. Conventional Monte Carlo methods are inefficient, demanding an exorbitant number of…

Probability density function estimation with weighted samples is the main foundation of all adaptive importance sampling algorithms. Classically, a target distribution is approximated either by a non-parametric model or within a parametric…

We review two recently developed efficient methods for calculating rate constants of processes dominated by rare events in high-dimensional complex systems. The first is transition interface sampling (TIS), based on the measurement of…

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…

We propose an instance-wise adaptive sampling framework for constructing compact and informative training datasets for supervised learning of inverse problem solutions. Typical learning-based approaches aim to learn a general-purpose…

Computing the exact likelihood of data in large Bayesian networks consisting of thousands of vertices is often a difficult task. When these models contain many deterministic conditional probability tables and when the observed values are…

In this work, we analyze an efficient sampling-based algorithm for general-purpose reachability analysis, which remains a notoriously challenging problem with applications ranging from neural network verification to safety analysis of…

We develop a novel computational method for evaluating the extreme excursion probabilities arising from random initialization of nonlinear dynamical systems. The method uses excursion probability theory to formulate a sequence of Bayesian…

Some classical uncertainty quantification problems require the estimation of multiple expectations. Estimating all of them accurately is crucial and can have a major impact on the analysis to perform, and standard existing Monte Carlo…

The fate of scientific hypotheses often relies on the ability of a computational model to explain the data, quantified in modern statistical approaches by the likelihood function. The log-likelihood is the key element for parameter…

Causal phenomena associated with rare events occur across a wide range of engineering problems, such as risk-sensitive safety analysis, accident analysis and prevention, and extreme value theory. However, current methods for causal…

The development of enhanced sampling methods has greatly extended the scope of atomistic simulations, allowing long-time phenomena to be studied with accessible computational resources. Many such methods rely on the identification of an…

To ensure that real-world infrastructure is safe and durable, systems are designed to not fail for any but the most rarely occurring parameter values. By only happening deep in the tails of the parameter distribution, failure probabilities…

Multiple importance sampling (MIS) methods use a set of proposal distributions from which samples are drawn. Each sample is then assigned an importance weight that can be obtained according to different strategies. This work is motivated by…

Running a reliability analysis on engineering problems involving complex numerical models can be computationally very expensive, requiring advanced simulation methods to reduce the overall numerical cost. Gaussian process based active…

The aim of survey statistics is to produce estimates with a minimal bias and a corresponding acceptable variance given a specific budget, preferable with a minor response burden for the participants. In recent years, considerable efforts…

To address the challenges of imbalanced multi-class datasets typically used for rare event detection in critical cyber-physical systems, we propose an optimal, efficient, and adaptable mixed integer programming (MIP) ensemble weighting…

Rare events in molecular dynamics are often related to noise-induced transitions between different macroscopic states (e.g., in protein folding). A common feature of these rare transitions is that they happen on timescales that are on…

The detection and analysis of events within massive collections of time-series has become an extremely important task for time-domain astronomy. In particular, many scientific investigations (e.g. the analysis of microlensing and other…

We propose and analyze a generalized splitting method to sample approximately from a distribution conditional on the occurrence of a rare event. This has important applications in a variety of contexts in operations research, engineering,…