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

Sammanfattning: 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.