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In hydrology, modeling streamflow remains a challenging task due to the limited availability of basin characteristics information such as soil geology and geomorphology. These characteristics may be noisy due to measurement errors or may be…
Article describes the results of the development and using of Rare-Event Monte-Carlo Simulation Algorithms for Dynamic Fault Trees Estimation. For Fault Trees estimation usually analytical methods are used (Minimal Cut sets, Markov Chains,…
We provide a general constrained risk inequality that applies to arbitrary non-decreasing losses, extending a result of Brown and Low [Ann. Stat. 1996]. Given two distributions $P_0$ and $P_1$, we find a lower bound for the risk of…
We describe and analyze a variance reduction approach for Monte Carlo (MC) sampling that accelerates the estimation of statistics of computationally expensive simulation models using an ensemble of models with lower cost. These lower cost…
This paper explores the effects of simulated moments on the performance of inference methods based on moment inequalities. Commonly used confidence sets for parameters are level sets of criterion functions whose boundary points may depend…
The objective of Bayesian inference is often to infer, from data, a probability measure for a random variable that can be used as input for Monte Carlo simulation. When datasets for Bayesian inference are small, a principle challenge is…
We present a practical implementation of a Monte Carlo method to estimate the significance of cross-correlations in unevenly sampled time series of data, whose statistical properties are modeled with a simple power-law power spectral…
Inverse rendering aims to recover scene geometry, material properties, and lighting from multi-view images. Given the complexity of light-surface interactions, importance sampling is essential for the evaluation of the rendering equation,…
Estimating risk measures such as large loss probabilities and Value-at-Risk is fundamental in financial risk management and often relies on computationally intensive nested Monte Carlo methods. While Multi-Level Monte Carlo (MLMC)…
Continuous level Monte Carlo is an unbiased, continuous version of the celebrated multilevel Monte Carlo method. The approximation level is assumed to be continuous resulting in a stochastic process describing the quantity of interest.…
High-speed boundary-layer transition is extremely sensitive to the free-stream disturbances which are often uncertain. This uncertainty compromises predictions of models and simulations. To enhance the fidelity of simulations, we directly…
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…
Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular non-parametric density estimators, the mean integrated square error converges…
The efficiency of Monte Carlo samplers is dictated not only by energetic effects, such as large barriers, but also by entropic effects that are due to the sheer volume that is sampled. The latter effects appear in the form of an entropic…
In this paper, we develop a computational approach for estimating the mean value of a quantity in the presence of uncertainty. We demonstrate that, under some mild assumptions, the upper and lower bounds of the mean value are efficiently…
Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo…
In this paper, we provide finite sample results to assess the consistency of Generalized Pareto regression trees, as tools to perform extreme value regression. The results that we provide are obtained from concentration inequalities, and…
In Bayesian inference, we seek to compute information about random variables such as moments or quantiles on the basis of {available data} and prior information. When the distribution of random variables is {intractable}, Monte Carlo (MC)…
Estimating the expectation of a real-valued function of a random variable from sample data is a critical aspect of statistical analysis, with far-reaching implications in various applications. Current methodologies typically assume…
Uncertainty in return level estimates for rare events, like the intensity of large rainfall events, makes it difficult to develop strategies to mitigate related hazards, like flooding. Latent spatial extremes models reduce uncertainty by…