Randomization, Bootstrap and Monte Carlo Methods in Biology

Randomization, Bootstrap and Monte Carlo Methods in Biology, Second Edition features new material on on bootstrap confidence intervals and significance testing, and incorporates new developments on the treatments of randomization methods for regression and analysis variation, including descriptions of applications of these methods in spreadsheet programs such as Lotus and other commercial packages. This second edition illustrates the value of modern computer intensive methods in the solution of a wide range of problems, with particular emphasis on biological applications. Examples given in the text include the controversial topic of whether there is periodicity between co-occurrences of species on islands.

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