This paper describes a new algorithm for Monte Carlo integration, based on the Field Estimator for Arbitrary Spaces (FiEstAS). The algorithm is discussed in detail, and its performance is evaluated in the context of Bayesian analysis, with emphasis on multimodal distributions with strong parameter degeneracies. Source code is available upon request.

The splitting of Quasi-Monte Carlo (QMC) point sequences into interleaved substreams has been suggested to raise the speed of distributed numerical integration and to lower the traffic on the network. The usefulness of this approach in GRID environments is discussed. After specifying requirements for using QMC techniques in GRID environments in general we review and evaluate the proposals made ...

Quasi-Monte Carlo (QMC) methods are being adopted in statistical applications due to the increasingly challenging nature of numerical integrals that are now routinely encountered. For integrands with d-dimensions and derivatives of order α, an optimal QMC rule converges at a best-possible rate O(N−α/d). However, in applications the value of α can be unknown and/or a rate-optimal QMC rule can be...

The simulation of light transport often involves specular and transmissive surfaces, which are modeled by functions that are not square integrable. However, in many practical cases unbiased Monte Carlo methods are not able to handle such functions efficiently and consistent Monte Carlo methods are applied. Based on quasi-Monte Carlo integration, a deterministic alternative to the stochastic app...

Monte Carlo integration of multi-dimensional Gaussian functions is widely applicable in the statistical analysis of functions of many variables, and such analysis is encountered in many fields of science. In this write-up, we compare two Monte Carlo integration algorithms from the Cuba library, Vegas, and Suave, in terms of convergence time and accuracy of evaluation of a multi-dimensional Gaus...

Lattice rules are a quasi-Monte Carlo method, an alternative to the Monte Carlo method for multidimensional numerical integration. The measures of performance that we estimate by simulation can be seen as the values of integrals in large dimensions. Therefore, instead of the usual Monte Carlo method, one can use lattice rules in simulation. In this paper, we compare these rules to the Monte Car...

monte carlo methods designed base on stochastic reiterations and can be useful in uncertainty conditions. the purpose of this research was investigation of uncertainty to rank desertification indicators. in order to decrease uncertainty have been applied monte carlo reiterations for each value of indicator, if rank of xi is higher than rank of xk constantly. using multi dimension integrals the ...

The Monte Carlo method has long been recognised as a powerful technique for performing certain calculations, generally those too complicated for a more classical approach. Since the use of high-speed computers became widespread in the 1950s, a great deal of theoretical investigation has been undertaken and practical experience has been gained in the Monte Carlo approach. The aim of this review ...

A brief review of the semi-classical Monte Carlo method for semiconductor device simulation is given, covering the standard Monte Carlo algorithms, variance reduction techniques, the self-consistent solution, and the physical semiconductor model including band structure and scattering mechanisms. The link between physically-based Monte Carlo methods and the numerical method of Monte Carlo integ...

We present photon beam diffusion, an efficient numerical method for accurately rendering translucent materials. Our approach interprets incident light as a continuous beam of photons inside the material. Numerically integrating diffusion from such extended sources has long been assumed computationally prohibitive, leading to the ubiquitous single-depth dipole approximation and the recent analyt...