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Randomization and Monte Carlo methods in biology. (English) Zbl 0726.92001

London etc.: Chapman and Hall. xiii, 281 p. £27.50 (1991).
Randomization methods can be used to test hypotheses and to determine confidence limits for parameters. Randomization testing involves determining the significance level of a test statistic calculated for an observed set of data by comparing the statistic with the distribution of the values. Randomization confidence limits for a parameter are given by the range of values of that parameter for which randomization testing gives a nonsignificant result. Monte Carlo methods can also be used to test hypothesis and to construct confidence intervals.
The book contains 12 chapters. Chapter 1 introduces the ideas of randomization methods through some examples. Chapter 2 introduces Monte Carlo tests, and also the computer-intensive techniques of jackknifing and bootstrapping since these are used sometimes as alternatives to randomization. Chapter 3 discusses some general theoretical matters concerning randomization and Monte Carlo tests. Chapters 4-10 then cover the analysis of various standard types of data. Chapter 11 gives some examples of nonstandard situations where computer-intensive methods are seen to provide the best hope for statistical analysis. Chapter 11 gives some general comments on the methods covered in the book. In all chapters the emphasis is on applications to biology. In the last Chapter 12, conclusions regarding randomization methods, as well as bootstrap and Monte Carlo methods are presented. FORTRAN codes are provided for some calculations in the appendices to the chapters.

MSC:

92B15 General biostatistics
92-02 Research exposition (monographs, survey articles) pertaining to biology
65C05 Monte Carlo methods
62P10 Applications of statistics to biology and medical sciences; meta analysis
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
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