Download e-book for iPad: Computational Statistics (2nd Edition) (Wiley Series in by Geof H. Givens, Jennifer A. Hoeting

By Geof H. Givens, Jennifer A. Hoeting

ISBN-10: 0470533315

ISBN-13: 9780470533314

This new version keeps to function a entire consultant to trendy and classical equipment of statistical computing. The e-book is constituted of 4 major components spanning the field:

- Optimization
- Integration and Simulation
- Bootstrapping
- Density Estimation and Smoothing

Within those sections,each bankruptcy contains a finished creation and step by step implementation summaries to accompany the reasons of key tools. the hot version comprises up to date assurance and current subject matters in addition to new subject matters similar to adaptive MCMC and bootstrapping for correlated facts. The booklet site now contains complete R code for the complete ebook. There are broad routines, genuine examples, and priceless insights approximately the best way to use the equipment in perform.

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Extra resources for Computational Statistics (2nd Edition) (Wiley Series in Computational Statistics)

Example text

43) is called the detailed balance condition. 44) where πj is the jth element of π. The πj are the solutions of the following set of equations: πj ≥ 0, πi = 1, and πj = i∈S πi pij for each j ∈ S. 44) as follows. If X(1) , X(2) , . . 46) t=1 almost surely as n → ∞, provided Eπ {|h(X)|} exists [605]. This is one form of the ergodic theorem, which is a generalization of the strong law of large numbers. 8 COMPUTING 17 We have considered here only Markov chains for discrete state spaces. In Chapters 7 and 8 we will apply these ideas to continuous state spaces.

2 MULTIVARIATE PROBLEMS In a multivariate optimization problem we seek the optimum of a real-valued function g of a p-dimensional vector x = (x1 , . . , xp )T . At iteration t, denote the estimated (t) optimum as x(t) = (x1 , . . , xp(t) )T . Many of the general principles discussed above for the univariate case also apply for multivariate optimization. Algorithms are still iterative. Many algorithms take steps based on a local linearization of g derived from a Taylor series or secant approximation.

This convergence reflects the fundamental notion that the observed data should overwhelm any prior as n → ∞. Bayesian evaluation of hypotheses relies upon the Bayes factor. 32) with θ i denoting the parameters corresponding to the ith hypothesis. The quantity B2,1 is the Bayes factor; it represents the factor by which the prior odds are multiplied to produce the posterior odds, given the data. The hypotheses H1 and H2 need not be 12 CHAPTER 1 REVIEW nested as for likelihood ratio methods. The computation and interpretation of Bayes factors is reviewed in [365].

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Computational Statistics (2nd Edition) (Wiley Series in Computational Statistics) by Geof H. Givens, Jennifer A. Hoeting

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