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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…

Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…

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.…

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…

The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with…

Naive approaches to amortized inference in probabilistic programs with unbounded loops can produce estimators with infinite variance. This is particularly true of importance sampling inference in programs that explicitly include rejection…

Importance sampling is a Monte Carlo method that introduces a proposal distribution to sample the space according to the target distribution. Yet calibration of the proposal distribution is essential to achieving efficiency, thus the resort…

In many stochastic problems, the output of interest depends on an input random vector mainly through a single random variable (or index) via an appropriate univariate transformation of the input. We exploit this feature by proposing an…

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…

A new approach of obtaining stratified random samples from statistically dependent random variables is described. The proposed method can be used to obtain samples from the input space of a computer forward model in estimating expectations…

Importance Sampling (IS) is a widely used variance reduction technique for enhancing the efficiency of Monte Carlo methods, particularly in rare-event simulation and related applications. Despite its effectiveness, the performance of IS is…

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…

Annealed importance sampling is a means to assign equilibrium weights to a nonequilibrium sample that was generated by a simulated annealing protocol. The weights may then be used to calculate equilibrium averages, and also serve as an…

Model fitting is possibly the most extended problem in science. Classical approaches include the use of least-squares fitting procedures and maximum likelihood methods to estimate the value of the parameters in the model. However, in recent…

Grid search and random search are widely used techniques for hyperparameter tuning in machine learning, especially when gradient information is unavailable. In these methods, a finite set of candidate configurations is evaluated, and the…

Importance sampling is a promising variance reduction technique for Monte Carlo simulation based derivative pricing. Existing importance sampling methods are based on a parametric choice of the proposal. This article proposes an algorithm…

Models and methods that are able to accurately and efficiently predict the flows of low-speed rarefied gases are in high demand, due to the increasing ability to manufacture devices at micro and nano scales. One such model and method is a…

This work explores the nature of augmented importance sampling in safety-constrained model predictive control problems. When operating in a constrained environment, sampling based model predictive control and motion planning typically…

A central challenge to applying many off-policy reinforcement learning algorithms to real world problems is the variance introduced by importance sampling. In off-policy learning, the agent learns about a different policy than the one being…

Many methods are available for assessing the importance of omitted variables in linear regression. These methods typically make different, non-falsifiable assumptions. Hence the data alone cannot tell us which method is most appropriate.…