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Unformatted text preview: Christian Robert Universit´ e ParisDauphine and George Casella University of Florida Introducing Monte Carlo Methods with R Solutions to RandomlyNumbered Exercises January 15, 2010 Springer Berlin Heidelberg NewYork Hong Kong London Singapore Milan Paris Tokyo Preface The scribes didn’t have a large enough set from which to determine patterns. Brandon Sauderson The Hero of Ages This partial solution manual to our book Introducing Monte Carlo Methods with R , published by Springer Verlag in 2010, has been compiled from our own solutions and from homeworks written by the following ParisDauphine stu dents in the 2007 Master in Statistical Information Processing (TSI): Thomas Bredillet, Anne Sabourin, and Jiazi Tang. Whenever appropriate, the R code of those students has been identified by a # (C.) Name in the text. A few solu tions in Chapter 4 are also taken verbatim from the solution manual to Monte Carlo Statistical Methods compiled by Roberto Casarin from the University of Brescia. We are very thankful to those students for their contribution. We also incorporated in this manual indications about some typos found in the first printing that came to our attention while composing this solution manual have been indicated as well. Following the new “print on demand” strategy of Springer Verlag, these typos will not be found in the versions of the book purchased in the coming months and should thus be ignored. Reproducing the warning JeanMichel Marin and Christian P. Robert wrote at the start of the solution manual to Bayesian Core , let us stress here that some selfstudy readers of Introducing Monte Carlo Methods with R may come to the realisation that the solutions provided here are too sketchy for them because the way we wrote those solutions assumes some minimal familiarity with the maths, the probability theory and with the statistics be hind the arguments. There is unfortunately a limit to the time and to the efforts we can put in this solution manual and studying Introducing Monte Carlo Methods with R requires some prerequisites in maths (such as matrix algebra and Riemann integrals), in probability theory (such as the use of joint and conditional densities) and some bases of statistics (such as the notions of vi Preface inference, sufficiency and confidence sets) that we cannot cover here. Casella and Berger (2001) is a good reference in case a reader is lost with the “basic” concepts or sketchy math derivations. We obviously welcome solutions, comments and questions on possibly er roneous or ambiguous solutions, as well as suggestions for more elegant or more complete solutions: since this manual is distributed both freely and in dependently from the book, it can be updated and corrected [almost] in real time! Note however that the R codes given in the following pages are not opti mised because we prefer to use simple and understandable codes, rather than condensed and efficient codes, both for time constraints and for pedagogical...
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 Fall '11
 Womack
 Probability theory, ........., Discrete probability distribution, CDF

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