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 edition: updated information on regression and time series analysis, multivariate methods, survival and growth data as well as software for computational statistics; references that reflect recent developments in methodology and computing techniques; and additional references on new applications of computer-intensive methods in biology. Providing 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.
RANDOMIZATION
The Idea of a Randomization Test
Examples of Randomization Tests
Aspects of Randomization Testing Raised by the Examples
Confidence Limits by Randomization
Applications of Randomization in Biology and Related Areas
Randomization and Observational Studies
Chapter Summary
THE JACKKNIFE
The Jackknife Estimator
Applications of Jackknifing in Biology
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-t Intervals
Parametric Confidence Intervals
A Better Estimate of Bias
Bootstrap Tests of Significance
Balanced Bootstrap Sampling
Applications of Bootstrapping in Biology
Further Reading
Chapter Summary
MONTE CARLO METHODS
Monte Carlo Tests
Generalized Monte Carlo Tests
Implicit Statistical Models
Applications of Monte Carlo Methods in Biology
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
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 Variances
Other Aspects of Analysis of Variance
Further Reading
Chapter Summary
REGRESSION ANALYSIS
Simple Linear Regression
Randomizing Residuals
Testing for a Nonzero ß Value
Confidence Limits for ß
Multiple Linear Regression
Alternative Randomization Methods with Multiple Regression
Bootstrapping and Jackknifing with Regression
Further Reading
Chapter Summary
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
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
TIME SERIES
Randomization and Time Series
Randomization Tests for Serial Correlation
Randomization Tests for Trend
Randomization Tests for Periodicity
Irregularly Spaced Series
Tests on Times of Occurrence
Discussion on Procedures for Irregular Series
Bootstrap Methods
Monte Carlo Methods
Model-Based vs. Moving-Block Resampling
Further Reading
Chapter Summary
MULTIVARIATE DATA
Univariate and Multivariate Tests
Sample Mean Vectors and Covariance Matrices
Comparison of Sample Mean Vectors
Chi-Squared Analyses for Count Data
Comparison of Variations for Several Samples
Principal Components Analysis and Other
One-Sample Methods
Discriminant Function Analysis
Further Reading
Chapter Summary
SURVIVAL AND GROWTH DATA
Bootstrapping Survival Data
Bootstrapping for Variable Selection
Bootstrapping for Model Selection
Group Comparisons
Growth Data
Further Reading
Chapter Summary
NONSTANDARD SITUATIONS
The Construction of Tests in Nonstandard Situations
Species Co-Occurrences on Islands
Alternative Switching Algorithms
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
FINAL COMMENTS
Randomization
Bootstrapping
Monte Carlo Methods in General
Classical vs. Bayesian Inference
REFERENCES
APPENDIX: SOFTWARE FOR COMPUTER-INTENSIVE STATISTICS
INDEX
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