Development of new variance reduction methods based on weight window technique in RMC code

2016 ◽  
Vol 90 ◽  
pp. 197-203 ◽  
Author(s):  
Xiao Fan ◽  
Guohui Zhang ◽  
Kan Wang
Keyword(s):  
Variance Reduction ◽  
Window Technique ◽  
Weight Window ◽  
Reduction Methods

scholarly journals On the optimal importance process for piecewise deterministic Markov process

2019 ◽  
Vol 23 ◽  
pp. 893-921
Author(s):  
H. Chraibi ◽  
A. Dutfoy ◽  
T. Galtier ◽  
J. Garnier
Keyword(s):  
Importance Sampling ◽  
Simulation Study ◽  
Variance Reduction ◽  
Sampling Method ◽  
Piecewise Deterministic Markov Process ◽  
Importance Sampling Method ◽  
Markovian Processes ◽  
Component Systems ◽  
Reference Measure ◽  
Reduction Methods

In order to assess the reliability of a complex industrial system by simulation, and in reasonable time, variance reduction methods such as importance sampling can be used. We propose an adaptation of this method for a class of multi-component dynamical systems which are modeled by piecewise deterministic Markovian processes (PDMP). We show how to adapt the importance sampling method to PDMP, by introducing a reference measure on the trajectory space. This reference measure makes it possible to identify the admissible importance processes. Then we derive the characteristics of an optimal importance process, and present a convenient and explicit way to build an importance process based on theses characteristics. A simulation study compares our importance sampling method to the crude Monte-Carlo method on a three-component systems. The variance reduction obtained in the simulation study is quite spectacular.

A Method to Alleviate the Long History Problem Encountered in Monte Carlo Simulations via Weight Window Variance Reduction

2017 ◽  
Vol 36 (6) ◽  
pp. 204-212 ◽  
Author(s):  
Xingchen Nie ◽  
Jia Li ◽  
Yuxiao Wu ◽  
Hengquan Zhang ◽  
Songlin Liu ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Variance Reduction ◽  
Weight Window

scholarly journals Some variance reduction methods for numerical stochastic homogenization

2016 ◽  
Vol 374 (2066) ◽  
pp. 20150168 ◽  
Author(s):  
X. Blanc ◽  
C. Le Bris ◽  
F. Legoll
Keyword(s):  
Monte Carlo ◽  
Variance Reduction ◽  
Stochastic Homogenization ◽  
Numerical Homogenization ◽  
Variance Reduction Techniques ◽  
Reduction Techniques ◽  
Effective Coefficients ◽  
Engineering Sciences ◽  
Reduction Methods ◽  
The Cost

We give an overview of a series of recent studies devoted to variance reduction techniques for numerical stochastic homogenization. Numerical homogenization requires that a set of problems is solved at the microscale, the so-called corrector problems. In a random environment, these problems are stochastic and therefore need to be repeatedly solved, for several configurations of the medium considered. An empirical average over all configurations is then performed using the Monte Carlo approach, so as to approximate the effective coefficients necessary to determine the macroscopic behaviour. Variance severely affects the accuracy and the cost of such computations. Variance reduction approaches, borrowed from other contexts in the engineering sciences, can be useful. Some of these variance reduction techniques are presented, studied and tested here.

scholarly journals An Effective Hard Thresholding Method Based on Stochastic Variance Reduction for Nonconvex Sparse Learning

2020 ◽  
Vol 34 (02) ◽  
pp. 1585-1592
Author(s):  
Guannan Liang ◽  
Qianqian Tong ◽  
Chunjiang Zhu ◽  
Jinbo Bi
Keyword(s):  
Variance Reduction ◽  
Linear Convergence ◽  
Stochastic Gradient Descent ◽  
Batch Size ◽  
Sparse Learning ◽  
Risk Minimization ◽  
Hard Thresholding ◽  
Thresholding Method ◽  
Empirical Risk ◽  
Reduction Methods

We propose a hard thresholding method based on stochastically controlled stochastic gradients (SCSG-HT) to solve a family of sparsity-constrained empirical risk minimization problems. The SCSG-HT uses batch gradients where batch size is pre-determined by the desirable precision tolerance rather than full gradients to reduce the variance in stochastic gradients. It also employs the geometric distribution to determine the number of loops per epoch. We prove that, similar to the latest methods based on stochastic gradient descent or stochastic variance reduction methods, SCSG-HT enjoys a linear convergence rate. However, SCSG-HT now has a strong guarantee to recover the optimal sparse estimator. The computational complexity of SCSG-HT is independent of sample size n when n is larger than 1/ε, which enhances the scalability to massive-scale problems. Empirical results demonstrate that SCSG-HT outperforms several competitors and decreases the objective value the most with the same computational costs.

scholarly journals Efficient Variance Reduction for American Call Options Using Symmetry Arguments

2021 ◽  
Vol 14 (11) ◽  
pp. 504
Author(s):  
François-Michel Boire ◽  
R. Mark Reesor ◽  
Lars Stentoft
Keyword(s):  
Standard Deviation ◽  
Variance Reduction ◽  
Control Variates ◽  
Put Options ◽  
Call Options ◽  
Variance Reduction Techniques ◽  
Reduction Techniques ◽  
Simulation Based ◽  
Out Of Sample ◽  
Reduction Methods

Recently it was shown that the estimated American call prices obtained with regression and simulation based methods can be significantly improved on by using put-call symmetry. This paper extends these results and demonstrates that it is also possible to significantly reduce the variance of the estimated call price by applying variance reduction techniques to corresponding symmetric put options. First, by comparing performance for pairs of call and (symmetric) put options for which the solution coincides, our results show that efficiency gains from variance reduction methods are different for calls and symmetric puts. Second, control variates should always be used and is the most efficient method. Furthermore, since control variates is more effective for puts than calls, and since symmetric pricing already offers some variance reduction, we demonstrate that drastic reductions in the standard deviation of the estimated call price is obtained by combining all three variance reduction techniques in a symmetric pricing approach. This reduces the standard deviation by a factor of over 20 for long maturity call options on highly volatile assets. Finally, we show that our findings are not particular to using in-sample pricing but also hold when using an out-of-sample pricing approach.

scholarly journals Variance-Reduction Methods for Monte Carlo Simulation of Radiation Transport

2021 ◽  
Vol 9 ◽  
Author(s):  
Salvador García-Pareja ◽  
Antonio M. Lallena ◽  
Francesc Salvat
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Variance Reduction ◽  
Radiation Transport ◽  
Scattering Method ◽  
Variance Reduction Techniques ◽  
Simulation Efficiency ◽  
Reduction Techniques ◽  
Exponential Transform ◽  
Reduction Methods

After a brief description of the essentials of Monte Carlo simulation methods and the definition of simulation efficiency, the rationale for variance-reduction techniques is presented. Popular variance-reduction techniques applicable to Monte Carlo simulations of radiation transport are described and motivated. The focus is on those techniques that can be used with any transport code, irrespective of the strategies used to track charged particles; they operate by manipulating either the number and weights of the transported particles or the mean free paths of the various interaction mechanisms. The considered techniques are 1) splitting and Russian roulette, with the ant colony method as builder of importance maps, 2) exponential transform and interaction-forcing biasing, 3) Woodcock or delta-scattering method, 4) interaction forcing, and 5) proper use of symmetries and combinations of different techniques. Illustrative results from analog simulations (without recourse to variance-reduction) and from variance-reduced simulations of various transport problems are presented.

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