Randomization, Bootstrap and Monte Carlo Methods in Biology, Third Edition

Modern computer-intensive statistical methods play a key role in solving many problems across a wide range of scientific disciplines. This new edition of the bestselling Randomization, Bootstrap and Monte Carlo Methods in Biology illustrates the value of a number of these methods with an emphasis on biological applications. This textbook focuses on three related areas in computational statistics: randomization, bootstrapping, and Monte Carlo methods of inference. The author emphasizes the sampling approach within randomization testing and confidence intervals. Similar to randomization, the book shows how bootstrapping, or resampling, can be used for confidence intervals and tests of significance. It also explores how to use Monte Carlo methods to test hypotheses and construct confidence intervals.New to the Third EditionUpdated information on regression and time series analysis, multivariate methods, survival and growth data as well as software for computational statisticsReferences that reflect recent developments in methodology and computing techniquesAdditional references on new applications of computer-intensive methods in biologyProviding comprehensive coverage of computer-intensive applications while also offering data sets online, Randomization, Bootstrap and Monte Carlo Methods in Biology, Third Edition supplies a solid foundation for the ever-expanding field of statistics and quantitative analysis in biology.

RANDOMIZATIONThe Idea of a Randomization TestExamples of Randomization TestsAspects of Randomization Testing Raised by the ExamplesConfidence Limits by RandomizationApplications of Randomization in Biology and Related AreasRandomization and Observational StudiesChapter SummaryTHE JACKKNIFEThe Jackknife EstimatorApplications of Jackknifing in BiologyChapter SummaryTHE BOOTSTRAPResampling with ReplacementStandard Bootstrap Confidence LimitsSimple Percentile Confidence LimitsBias-Corrected Percentile Confidence LimitsAccelerated Bias-Corrected Percentile Limits Other Methods for Constructing Confidence IntervalsTransformations to Improve Bootstrap-t IntervalsParametric Confidence Intervals A Better Estimate of BiasBootstrap Tests of SignificanceBalanced Bootstrap SamplingApplications of Bootstrapping in BiologyFurther ReadingChapter SummaryMONTE CARLO METHODSMonte Carlo TestsGeneralized Monte Carlo TestsImplicit Statistical ModelsApplications of Monte Carlo Methods in BiologyChapter SummarySOME GENERAL CONSIDERATIONSQuestions about Computer-Intensive Methods Power Number of Random Sets of Data Needed for a TestDetermining a Randomization Distribution Exactly The Number of Replications for Confidence IntervalsMore Efficient Bootstrap Sampling MethodsThe Generation of Pseudo-Random NumbersThe Generation of Random PermutationsChapter SummaryONE- AND TWO-SAMPLE TESTS The Paired Comparisons Design The One-Sample Randomization TestThe Two-Sample Randomization Test Bootstrap TestsRandomizing ResidualsComparing the Variation in Two SamplesA Simulation Study The Comparison of Two Samples on Multiple MeasurementsFurther ReadingChapter SummaryANALYSIS OF VARIANCEOne-Factor Analysis of VarianceTests for Constant Variance Testing for Mean Differences Using ResidualsExamples of More Complicated Types of Analysis of Variance Procedures for Handling Unequal VariancesOther Aspects of Analysis of VarianceFurther ReadingChapter SummaryREGRESSION ANALYSISSimple Linear Regression Randomizing Residuals Testing for a Nonzero ß ValueConfidence Limits for ßMultiple Linear RegressionAlternative Randomization Methods with Multiple RegressionBootstrapping and Jackknifing with RegressionFurther ReadingChapter SummaryDISTANCE MATRICES AND SPATIAL DATATesting for Association between Distance MatricesThe Mantel TestSampling the Randomization DistributionConfidence Limits for Regression CoefficientsThe Multiple Mantel TestOther Approaches with More Than Two MatricesFurther ReadingChapter SummaryOTHER ANALYSES ON SPATIAL DATASpatial Data AnalysisThe Study of Spatial Point PatternsMead's Randomization TestTests for Randomness Based on DistancesTesting for an Association between Two Point PatternsThe Besag-Diggle Test Tests Using Distances Between Points Testing for Random MarkingFurther ReadingChapter SummaryTIME SERIES Randomization and Time SeriesRandomization Tests for Serial CorrelationRandomization Tests for TrendRandomization Tests for PeriodicityIrregularly Spaced SeriesTests on Times of Occurrence Discussion on Procedures for Irregular Series Bootstrap Methods Monte Carlo Methods Model-Based vs. Moving-Block ResamplingFurther ReadingChapter SummaryMULTIVARIATE DATAUnivariate and Multivariate TestsSample Mean Vectors and Covariance Matrices Comparison of Sample Mean VectorsChi-Squared Analyses for Count DataComparison of Variations for Several SamplesPrincipal Components Analysis and OtherOne-Sample MethodsDiscriminant Function Analysis Further ReadingChapter Summary SURVIVAL AND GROWTH DATA Bootstrapping Survival Data Bootstrapping for Variable SelectionBootstrapping for Model SelectionGroup ComparisonsGrowth DataFurther ReadingChapter SummaryNONSTANDARD SITUATIONSThe Construction of Tests in Nonstandard Situations Species Co-Occurrences on Islands Alternative Switching AlgorithmsExamining Time Changes in Niche Overlap Probing Multivariate Data with Random SkewersAnt Species Sizes in Europe Chapter Summary BAYESIAN METHODS The Bayesian Approach to Data Analysis The Gibbs Sampler and Related Methods Biological ApplicationsFurther ReadingChapter Summary FINAL COMMENTSRandomization Bootstrapping Monte Carlo Methods in GeneralClassical vs. Bayesian InferenceREFERENCESAPPENDIX: SOFTWARE FOR COMPUTER-INTENSIVE STATISTICSINDEX

Bryan F.J. Manly (University of Otago, Dunedin, New Zealand), Jorge A. Navarro Alberto