Related papers: Monte Carlo Estimation for Imprecise Probabilities…

An introduction to the basics of Monte Carlo is given. The topics covered include, sample space, events, probabilities, random variables, mean, variance, covariance, characteristic function, chebyshev inequality, law of large numbers,…

Large deviation theory has provided important clues for the choice of importance sampling measures for Monte Carlo evaluation of exceedance probabilities. However, Glasserman and Wang [Ann. Appl. Probab. 7 (1997) 731--746] have given…

Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable.…

Given a smooth function $f$, we develop a general approach to turn Monte Carlo samples with expectation $m$ into an unbiased estimate of $f(m)$. Specifically, we develop estimators that are based on randomly truncating the Taylor series…

In this paper, we introduce a new technique that combines two popular methods to estimate uncertainty in object detection. Quantifying uncertainty is critical in real-world robotic applications. Traditional detection models can be ambiguous…

This paper concerns numerical assessment of Monte Carlo error in particle filters. We show that by keeping track of certain key features of the genealogical structure arising from resampling operations, it is possible to estimate variances…

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…

Metrics of model goodness-of-fit, model comparison, and model parameter estimation are the main categories of statistical problems in science. Bayesian and frequentist methods that address these questions often rely on a likelihood…

A natural Monte Carlo method to approximate conditional expectations in a probabilistic framework is justified by a general result inspired on the Besicovitch covering theorem on differentiation of measures. The method is specially useful…

Monte-Carlo simulations are routinely used for estimating the scaling exponents of complex systems. However, due to finite-size effects, determining the exponent values is often difficult and not reliable. Here we present a novel technique…

Complex scientific models where the likelihood cannot be evaluated present a challenge for statistical inference. Over the past two decades, a wide range of algorithms have been proposed for learning parameters in computationally feasible…

Quantiles and expected shortfalls are usually used to measure risks of stochastic systems, which are often estimated by Monte Carlo methods. This paper focuses on the use of quasi-Monte Carlo (QMC) method, whose convergence rate is…

In Monte Carlo integration an accurate and reliable determination of the numerical intregration error is essential. We point out the need for an independent estimate of the error on this error, for which we present an unbiased estimator. In…

A Monte Carlo model was used to study the scattering error of an absorption meter with a divergent light beam and a limited acceptance angle of the receiver. Reflections at both ends of the tube were taken into account. Calculations of the…

Monte Carlo simulations of diffusion processes often introduce bias in the final result, due to time discretization. Using an auxiliary Poisson process, it is possible to run simulations which are unbiased. In this article, we propose such…

Estimating the density of a continuous random variable X has been studied extensively in statistics, in the setting where n independent observations of X are given a priori and one wishes to estimate the density from that. Popular methods…

We present a Monte Carlo method to compute efficiently susceptibilites or covariances of two physical variables. The method relies on a generalization of the exchange cluster algorithm to any model of interacting particles with any $2$-body…

Importance sampling has been known as a powerful tool to reduce the variance of Monte Carlo estimator for rare event simulation. Based on the criterion of minimizing the variance of Monte Carlo estimator within a parametric family, we…

Approximate Bayesian Computation (ABC) is a powerful method for carrying out Bayesian inference when the likelihood is computationally intractable. However, a drawback of ABC is that it is an approximate method that induces a systematic…

Beta regression models provide an adequate approach for modeling continuous outcomes limited to the interval (0,1). This paper deals with an extension of beta regression models that allow for explanatory variables to be measured with error.…