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A First Course in Monte Carlo 1st Edition

by George Fishman (Author)
2.5 out of 5 stars 2 customer reviews
ISBN-13: 978-0534420468
ISBN-10: 053442046X
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Product Details

  • Hardcover: 350 pages
  • Publisher: Duxbury Press; 1 edition (October 5, 2005)
  • Language: English
  • ISBN-10: 053442046X
  • ISBN-13: 978-0534420468
  • Product Dimensions: 7.5 x 0.8 x 9.5 inches
  • Shipping Weight: 9.6 ounces (View shipping rates and policies)
  • Average Customer Review: 2.5 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #1,599,366 in Books (See Top 100 in Books)

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4.0 out of 5 starsA very good first introduction to Monte Carlo
By Todd Ebert on December 16, 2007
Format: Hardcover
A first course in Monte Carlo offers an introduction to Monte Carlo sampling, a very important topic in both statistics and computer science. Monte Carlo sampling can be described as follows. Suppose one has a function f(x) that is defined over a state space X. Two common problems are to
i) determine the integeral/expectancy of f over the state space, and
ii) find a value x* in the space for which f(x*) <= f(x) for all x in X.

In this text Fishman presents how to approximate the solutions to both problems via Monte Carlo sampling; both independent Monte Carlo and Markov chain Monte Carlo sampling. Independent Monte Carlo sampling involves using a probability distribution w(x) over X to randomly generate n sample points x1,...,xn and then e.g. approximate the expectancy of f over the space by averaging the values
(f/w)(x1),...,(f/w)(xn). Statistically one can show that the average will converge to the desired value as n is allowed to increase. Chapter 2 discusses this method in good detail. I especially appreciated his discussion on the cost of generating a sample, along with the variance of the function values evaluated at the sample points, and the trade-off that ensues when one attempts to reduce variance (i.e. obtain faster convergence) at a cost of a more costly sampling technique. He then goes on to state a very useful fact with respect to two different sampling plans, in that the better plan will induce CR * VR < 1, where CR and VR are the cost and variance ratios of the two plans (I'm assuming the better plan is in the numerator of both ratios). This result applies to both problems i) and ii) above, and can be used as a means for testing the merit of a new sampling/optimization technique relative to some existing one.Read more ›
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1.0 out of 5 starsA first course in Monte Carlo
By Kimberlie Gonzales on June 1, 2009
Format: Hardcover
Horrible, I waited a month to get this book after I placed the order and I never received this book. I tried communicating with the seller on the status of my order and never heard back. Horrible service!!!!!!!!!!!!!!!
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