Introduction to Monte Carlo methods

TL;DR

This paper provides an introductory overview of Monte Carlo methods, including integration, random number generation, and sampling techniques, with applications in high energy physics.

Contribution

It introduces classical quadrature, variance reduction, pseudo-random and quasi-random numbers, and sampling algorithms like Metropolis for high energy physics applications.

Findings

Overview of Monte Carlo integration and variance reduction techniques

Description of pseudo-random and quasi-random number generation methods

Discussion of algorithms for phase space sampling in high energy collisions

Abstract

These lectures given to graduate students in high energy physics, provide an introduction to Monte Carlo methods. After an overview of classical numerical quadrature rules, Monte Carlo integration together with variance-reducing techniques is introduced. A short description on the generation of pseudo-random numbers and quasi-random numbers is given. Finally, methods to generate samples according to a specified distribution are discussed. Among others, we outline the Metropolis algorithm and give an overview of existing algorithms for the generation of the phase space of final state particles in high energy collisions.