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Exploring the Impact of Pseudo and Quasi Random Number Generators on Monte Carlo Integration of the Multivariate Normal Distribution

Stolz, Marcus LU and Christopher, Jonathan LU (2024) STAH11 20232
Department of Statistics
Abstract
This thesis examines the effects of pseudo and quasi-random number generators on the accuracy and efficiency of Monte Carlo Integration in the case of the multivariate normal distribution. The study compares the performance of the Mersenne Twister (a pseudo-random number generator) with Sobol and Halton sequences (quasi-random number generators). By evaluating these generators across different dimensions and scenarios, the research aims to determine their impact on the behaviour of Monte Carlo Integration. Our findings indicate notable differences in the variance of estimates. In cases involving integration of the distribution’s "bump," the Sobol sequence exhibits higher variance, suggesting sensitivity to specific distributional... (More)
This thesis examines the effects of pseudo and quasi-random number generators on the accuracy and efficiency of Monte Carlo Integration in the case of the multivariate normal distribution. The study compares the performance of the Mersenne Twister (a pseudo-random number generator) with Sobol and Halton sequences (quasi-random number generators). By evaluating these generators across different dimensions and scenarios, the research aims to determine their impact on the behaviour of Monte Carlo Integration. Our findings indicate notable differences in the variance of estimates. In cases involving integration of the distribution’s "bump," the Sobol sequence exhibits higher variance, suggesting sensitivity to specific distributional characteristics. Additionally, in the bivariate case, extreme correlations result in increased variance, particularly for Sobol sequences. An interesting result is that from the fifth dimension onward, the Halton sequence demonstrates a notable increase in computational demand compared to the other generators. Due to computational constraints, we have been unable to go beyond 7 dimensions. This thesis contributes to the field of computational statistics by providing insights into the optimal choice of random number generators for Monte Carlo methods in multivariate statistical analysis. (Less)
Please use this url to cite or link to this publication:
author
Stolz, Marcus LU and Christopher, Jonathan LU
supervisor
organization
course
STAH11 20232
year
type
M2 - Bachelor Degree
subject
keywords
Monte Carlo integration, Quasi monte carlo integration, Random number generation
language
English
id
9146881
date added to LUP
2024-02-13 12:23:00
date last changed
2024-02-13 12:23:00
@misc{9146881,
  abstract     = {{This thesis examines the effects of pseudo and quasi-random number generators on the accuracy and efficiency of Monte Carlo Integration in the case of the multivariate normal distribution. The study compares the performance of the Mersenne Twister (a pseudo-random number generator) with Sobol and Halton sequences (quasi-random number generators). By evaluating these generators across different dimensions and scenarios, the research aims to determine their impact on the behaviour of Monte Carlo Integration. Our findings indicate notable differences in the variance of estimates. In cases involving integration of the distribution’s "bump," the Sobol sequence exhibits higher variance, suggesting sensitivity to specific distributional characteristics. Additionally, in the bivariate case, extreme correlations result in increased variance, particularly for Sobol sequences. An interesting result is that from the fifth dimension onward, the Halton sequence demonstrates a notable increase in computational demand compared to the other generators. Due to computational constraints, we have been unable to go beyond 7 dimensions. This thesis contributes to the field of computational statistics by providing insights into the optimal choice of random number generators for Monte Carlo methods in multivariate statistical analysis.}},
  author       = {{Stolz, Marcus and Christopher, Jonathan}},
  language     = {{eng}},
  note         = {{Student Paper}},
  title        = {{Exploring the Impact of Pseudo and Quasi Random Number Generators on Monte Carlo Integration of the Multivariate Normal Distribution}},
  year         = {{2024}},
}