We study Monte Carlo approximations to high dimensional parameter dependent integrals. We survey the multilevel variance reduction technique introduced by the author in [4] and present extensions and new developments of it. The tools needed for the convergence analysis of vector-valued Monte Carlo methods are discussed, as well. Applications to stochastic solution of integral equations are give...

We have applied the IRMC method to the 3-D, 1T, nonlinear radiation diffusion equation. A multimaterial duct problem is shown in Fig. 1. This problem features a 0.5 keV blackbody flux on the low-x side. Radiation is propagated through a doglegged duct bounded by an opaque wall. An optically thick foil is placed on the high-y side of the outlet. A contour plot of the solution is shown in Fig. 2,...

Bayesian inference often requires integrating some function with respect to a posterior distribution. Monte Carlo methods are sampling algorithms that allow to compute these integrals numerically when they are not analytically tractable. We review here the basic principles and the most common Monte Carlo algorithms, among which rejection sampling, importance sampling and Monte Carlo Markov chai...

background: palladium-103 (103pd) is a brachytherapy source for cancer treatment. the monte carlo codes are usually applied for dose distribution and effect of shieldings. monte carlo calculation of dose distribution in water phantom due to a med3633 103pd source is presented in this work. materials and methods: the dose distribution around the 103pd model med3633 located in the center of 30×30...

I discuss optimized data analysis and Monte Carlo methods. Reweighting methods are discussed through examples, like Lee-Yang zeroes in the Ising model and the absence of deconfinement in QCD. I discuss reweighted data analysis and multi-hystogramming. I introduce Simulated Tempering, and as an example its application to the Random Field Ising Model. I illustrate Parallel Tempering, and discuss ...

so that the error in I goes down as 1/ √ M and is smaller if the variance σ 2 f of f is smaller. For a one dimensional integration the Monte Carlo method is not compelling. However consider a d dimensional integral evaluated withM points. For a uniform mesh each dimension of the integral getsM1/d points, so that the separation is h = M−1/d . The error in the integration over one h cube is of or...

Monte Carlo methods comprise a large and still growing collection of methods of repetitive simulation designed to obtain approximate solutions of various problems by playing games of chance. Often these methods are motivated by randomness inherent in the problem being studied (as, e.g., when simulating the random walks of “particles” undergoing diffusive transport), but this is not an essential...

Actuality Programs on the basis of Monte Carlo simulation allow to perform computer experiments in various areas of modern physics, such as: nuclear physics, high-energy physics, cosmic rays, neutrino physics. Such experiments are necessary to better understand the nature of processes, to make forecasts concerning real experiments. But also application of these packages of interest increases in...

In this paper, the pricing of a European call option on the underlying asset is performed by using a Monte Carlo method, one of the powerful simulation methods, where the price development of the asset is simulated and value of the claim is computed in terms of an expected value. The proposed approach, applied in Monte Carlo simulation, is based on the Black-Scholes equation which generally def...