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Monte Carlo

Concepts, Algorithms, and Applications

  • Textbook
  • © 1996

Overview

Authors:
  1. George S. Fishman

    1. Department of Operations Research, University of North Carolina, Chapel Hill, USA

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  • Monte Carlo methods are widely used techniques, with applications in operations research, engineering, and computing
  • The author covers all of the most important techniques of the Monte Carlo method
  • It demonstrates how to analyze the sampling results with a computer, including over 75 readily implementable algorithms

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xxv
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  2. Introduction

    • George S. Fishman
    Pages 1-12

  3. Estimating Volume and Count

    • George S. Fishman
    Pages 13-144

  4. Generating Samples

    • George S. Fishman
    Pages 145-254

  5. Increasing Efficiency

    • George S. Fishman
    Pages 255-334

  6. Random Tours

    • George S. Fishman
    Pages 335-491

  7. Designing and Analyzing Sample Paths

    • George S. Fishman
    Pages 493-586

  8. Generating Pseudorandom Numbers

    • George S. Fishman
    Pages 587-682

  9. Back Matter

    Pages 683-698
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Keywords

About this book

This book provides an introduction to the Monte Carlo method suitable for a one-or two-semester course for graduate and advanced undergraduate students in the mathematical and engineering sciences. It also can serve as a reference for the professional analyst. In the past, my inability to provide students with a single­ source book on this topic for class and for later professional reference had left me repeatedly frustrated, and eventually motivated me to write this book. In addition to focused accounts of major topics, the book has two unifying themes: One concerns the effective use of information and the other concerns error control and reduction. The book describes how to incorporate information about a problem into a sampling plan in a way that reduces the cost of estimating its solution to within a specified error bound. Although exploiting special structures to reduce cost long has been a hallmark of the Monte Carlo method, the propen­ sity of users of the method to discard useful information because it does not fit traditional textbook models repeatedly has impressed me. The present account aims at reducing the impediments to integrating this information. Errors, both statistical and computational, abound in every Monte Carlo sam­ pling experiment, and a considerable methodology exists for controlling them.

Authors and Affiliations

  • Department of Operations Research, University of North Carolina, Chapel Hill, USA

    George S. Fishman

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