Search results for "Variance reduction"
showing 5 items of 5 documents
Heretical Mutiple Importance Sampling
2016
Multiple Importance Sampling (MIS) methods approximate moments of complicated distributions by drawing samples from a set of proposal distributions. Several ways to compute the importance weights assigned to each sample have been recently proposed, with the so-called deterministic mixture (DM) weights providing the best performance in terms of variance, at the expense of an increase in the computational cost. A recent work has shown that it is possible to achieve a trade-off between variance reduction and computational effort by performing an a priori random clustering of the proposals (partial DM algorithm). In this paper, we propose a novel "heretical" MIS framework, where the clustering …
Unbiased Estimators and Multilevel Monte Carlo
2018
Multilevel Monte Carlo (MLMC) and unbiased estimators recently proposed by McLeish (Monte Carlo Methods Appl., 2011) and Rhee and Glynn (Oper. Res., 2015) are closely related. This connection is elaborated by presenting a new general class of unbiased estimators, which admits previous debiasing schemes as special cases. New lower variance estimators are proposed, which are stratified versions of earlier unbiased schemes. Under general conditions, essentially when MLMC admits the canonical square root Monte Carlo error rate, the proposed new schemes are shown to be asymptotically as efficient as MLMC, both in terms of variance and cost. The experiments demonstrate that the variance reduction…
A partially reflecting random walk on spheres algorithm for electrical impedance tomography
2015
In this work, we develop a probabilistic estimator for the voltage-to-current map arising in electrical impedance tomography. This novel so-called partially reflecting random walk on spheres estimator enables Monte Carlo methods to compute the voltage-to-current map in an embarrassingly parallel manner, which is an important issue with regard to the corresponding inverse problem. Our method uses the well-known random walk on spheres algorithm inside subdomains where the diffusion coefficient is constant and employs replacement techniques motivated by finite difference discretization to deal with both mixed boundary conditions and interface transmission conditions. We analyze the global bias…
A Monte Carlo-based dosimetric characterization of Esteya® , an electronic surface brachytherapy unit
2018
PURPOSE The purpose of this work is threefold: First, to obtain the phase space of an electronic brachytherapy (eBT) system designed for surface skin treatments. Second, to explore the use of some efficiency enhancing (EFEN) strategies in the determination of the phase space. Third, to use the phase space previously obtained to perform a dosimetric characterization of the Esteya eBT system. METHODS The Monte Carlo study of the 69.5 kVp x-ray beam of the Esteya® unit (Elekta Brachytherapy, Veenendaal, The Netherlands) was performed with PENELOPE2014. The EFEN strategies included the use of variance reduction techniques and mixed Class II simulations, where transport parameters were fine-tune…
Variance Estimation and Asymptotic Confidence Bands for the Mean Estimator of Sampled Functional Data with High Entropy Unequal Probability Sampling …
2013
For fixed size sampling designs with high entropy it is well known that the variance of the Horvitz-Thompson estimator can be approximated by the Hajek formula. The interest of this asymptotic variance approximation is that it only involves the first order inclusion probabilities of the statistical units. We extend this variance formula when the variable under study is functional and we prove, under general conditions on the regularity of the individual trajectories and the sampling design, that it asymptotically provides a uniformly consistent estimator of the variance function of the Horvitz-Thompson estimator of the mean function. Rates of convergence to the true variance function are gi…