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Numerical Analysis for Statisticians (Statistics and Computing) Corrected Edition
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From a review:
"This book provides reasonably good coverage of numerical methods that are important in statistical applications. ...but overall the text serves as a good introduction to computational statistics."
From the Publisher
This book will be an important reference for all statisticians interested in computing and software development.
Top Customer Reviews
numerical analysis is intended to equip students to craft their own
software and to understand the advantages and disadvantages of different
numerical methods". Lets look at a few topics to see whether these
lofty goals were achieved.
Least-squares calculations: The chapter on linear regression is nine
pages. The largest section is on the sweep operator (the problems with
the sweep are not mentioned). Solving least squares is thru the normal
equations only (which numerical analysts agree is the least stable of
the "big three" methods for solving least squares problems). There is a
page on woodbury's formula for determinants. Who uses that!? So many
problems in statistics eventually boil down to a least-squares
calculation. This book has almost nothing useful to say about this
problem. How can students "craft their own software" after reading this
book? They simply can't. Look elsewhere.
Eigenvalues: The chapter on eigenvalues is eight pages and covers only
Jacobi's and the Rayleigh quotient, nothing on the QR, nothing on
bidiagonalization. The nine pages would have been better used for
Bootstrap calculations: I decided to check out section 22.5,
"importance sampling". After a so-so 2-page inroduction we get an
example. Example 22.5.1 uses the "Hormone Patch Data" from Efron and
Tibshirani's Bootstrap book (a wonderful book, by the way). First, the
analysis is botched, the numerator and denominator variables were
interchanged (relative to Efron and Tibshirani).Read more ›
The usual matrix algebra stuff for linear models is also there. You will also find a chapter on nonlinear equations and a chapter on splines. There are asymptotic expansions in Chapter 4 and Edgeworth expansions in Chapter 17. Almost everything that is important in statistical computing today is included.
This book can be used as for a graduate course in statistical computing and is a valuable reference for any statistical researcher.
From the above, it may sound as if Numerical Analysis for Statisticians does not fulfill its purpose and is too much of a mathematical book. Be assured this is not the case: the contents are firmly grounded in calculus (analysis) but the (numerical) algorithms are only one code away. An illustration (among many) is found in Section 8.4: Finding a Single Eigenvalue, where Kenneth Lange shows how the Raleigh quotient algorithm of the previous section can be exploited to this aim, when supplemented with a good initial guess based on Gerschgorin's circle theorem. This is brilliantly executed in two pages and the code is just one keyboard away. The EM algorithm is immersed into a larger MM perspective.Read more ›
Fortunately it turned out that it is not so difficult as I thought to "return" a mistaken Kindle purchase, via the "Manage my Kindle" page.
In conclusion: fantastic book, but make sure you get the second edition, and if you want an eBook version, don't buy it on Amazon for the time being!