Introduction

  • Luca Martino
  • David Luengo
  • Joaquín Míguez
Chapter
Part of the Statistics and Computing book series (SCO)

Abstract

This chapter provides an introduction to the different approaches available for sampling from a given probability distribution. We start with a brief history of the Monte Carlo (MC) method, one of the most influential algorithms of the twentieth century and the main driver for the current widespread use of random samples in many scientific fields. Then we discuss the need for MC approaches through a few selected examples, starting with two important classical applications (numerical integration and importance sampling), and finishing with two more recent developments (inverse Monte Carlo and quasi Monte Carlo). This is followed by a review of the three types of “random numbers” which can be generated (“truly” random, pseudo-random, and quasi-random), a brief description of some pseudo-random number generators and an overview of the different classes of random sampling methods available in the literature: direct, accept/reject, MCMC, importance sampling, and hybrid. Finally, the chapter concludes with an exposition of the motivation, goals, and organization of the book.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Luca Martino
    • 1
  • David Luengo
    • 2
  • Joaquín Míguez
    • 1
  1. 1.Department of Signal Theory and CommunicationsCarlos III University of MadridMadridSpain
  2. 2.Department of Signal Theory and CommunicationsTechnical University of MadridMadridSpain

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