Randomization, Bootstrap and Monte Carlo Methods in Biology

Preface to the Second Edition Preface to the First Edition Randomization The Idea of a Randomization Test Examples of Randomization Tests Aspects of Randomization Testing Raised by the Examples Sampling the Randomization Distribution or Systematic Enumeration Equivalent Test Statistics Significance Levels for Classical and Randomization Tests Limitations of Randomization Tests Confidence Limits by Randomization Applications of Randomization in Biology Single Species Ecology Genetics, Evolution and Natural Selection Community Ecology Randomization and Observational Studies Chapter Summary The Jackknife The Jackknife Estimator Applications of Jackknifing in Biology Single Species Analyses Genetics, Evolution and Natural Selection Community Ecology Chapter Summary The Bootstrap Resampling with Replacement Standard Bootstrap Confidence Limits Simple Percentile Confidence Limits Bias Corrected Percentile Confidence Limits Accelerated Bias Corrected Percentile Limits Other Methods for Constructing Confidence Intervals Transformations to Improve Bootstrap Intervals Parametric Confidence Intervals A Better Estimate of Bias Bootstrap Tests of Significance Balanced Bootstrap Sampling Applications of Bootstrapping in Biology Single Species Ecology Genetics, Evolution and Natural Selection Community Ecology Further Reading Chapter Summary Monte Carlo Methods Monte Carlo Tests Generalized Monte Carlo Tests Implicit Statistical Models Applications of Monte Carlo Methods in Biology Single Species Ecology Chapter Summary Some General Considerations Questions about Computer-Intensive Methods Power Number of Random Sets of Data Needed for a Test Determining a Randomization Distribution Exactly The number of replications for confidence intervals More Efficient Bootstrap Sampling Methods The Generation of Pseudo-Random Numbers The Generation of Random Permutations Chapter Summary One and Two Sample Tests The Paired Comparisons Design The One Sample Randomization Test The Two Sample Randomization Test Bootstrap Tests Randomizing Residuals Comparing the Variation in Two Samples A Simulation Study The Comparison of Two Samples on Multiple Measurements Further Reading Chapter Summary Exercises Analysis of Variance One Factor Analysis of Variance Tests for Constant Variance Testing for Mean Differences Using Residuals Examples of More Complicated Types of Analysis of Variance Procedures for Handling Unequal Group Variances Other Aspects of Analysis of Variance Further Reading Chapter Summary Exercises Regression Analysis Simple Linear Regression Randomizing Residuals Testing for a Non-Zero B Value Confidence Limits for B Multiple Linear Regression Alternative Randomization Methods with Multiple Regression Bootstrapping and Jackknifing with Regression Further Reading Chapter Summary Exercises Distance Matrices and Spatial Data Testing for Association between Distance Matrices The Mantel Test Sampling the Randomization Distribution Confidence Limits for Regression Coefficients The Multiple Mantel Test Other Approaches with More than Two Matrices Further Reading Chapter Summary Exercises Other Analyses on Spatial Data Spatial Data Analysis The Study of Spatial Point Patterns Mead's Randomization Test Tests for Randomness Based on Distances Testing for an Association between Two Point Patterns The Besag-Diggle Test Tests Using Distances between Points Testing for Random Marking Further Reading Chapter Summary Exercises Time Series Randomization and Time Series Randomization Tests for Serial Correlation Randomization T ests for Trend Randomization Tests for Periodicity Irregularly Spaced Series Tests on Times of Occurrence Discussion on Procedures for Irregular Series Bootstrap and Monte Carlo Tests Further Reading Chapter Summary Exercises Multivariate Data Univariate and Multivariate Tests Sample Means and Covariance Matrices Comparison of Sample Mean Vectors Chi-Squared Analyses for Count Data Principle Component Analysis and Other One Sample Methods Discriminant Function Analysis Further Reading Chapter Summary Exercises Survival and Growth Data Bootstrapping Survival Data Bootstrapping for Variable Selection Bootstrapping for Model Selection Group Comparisons Growth Data Further Reading Chapter Summary Exercises Non-Standard Situations The Construction of Tests in Non-Standard Situations Species Co-Occurrences on Islands An Alternative Generalized Monte Carlo Test Examining Time Changes in Niche Overlap Probing Multivariate Data with Random Skewers Ant Species Sizes in Europe Chapter Summary Bayesian Methods The Bayesian Approach to Data Analysis The Gibbs Sampler and Related Methods Biological Applications Further Reading Chapter Summary Exercises Conclusion and Final Comments Randomization Bootstrapping Monte Carlo Methods in General Classical versus Bayesian Inference Appendix Software for Computer Intensive Statistics References Index