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

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ISBN: 9781584885412 | 1584885416
Cover: Hardcover
Copyright: 8/15/2006

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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. It has been updated to reflect developments in methodology, computing, and applications and features extensively revised chapters on bootstrap and Monte Carlo methods that incorporate many new applications. The author also includes new information on time series, multivariate, survival, and growth data and provides an expanded appendix on software for computational statistics.

Chapter 1 Randomization

(28)

1.1 The Idea of a Randomization Test

(3)

1.2 Examples of Randomization Tests

(10)

1.3 Aspects of Randomization Testing Raised by the Examples

(4)

1.3.1 Sampling the Randomization Distribution or Systematic Enumeration

(1)

1.3.2 Equivalent Test Statistics

(1)

1.3.3 Significance Levels for Classical and Randomization Tests

(1)

1.3.4 Limitations of Randomization Tests

(1)

1.4 Confidence Limits by Randomization

(3)

1.5 Applications of Randomization in Biology and Related Areas

(4)

1.5.1 Single Species Ecology

(1)

1.5.2 Genetics, Evolution, and Natural Selection

(1)

1.5.3 Community Ecology

(2)

1.5.4 Other Environmental Applications

(1)

1.6 Randomization and Observational Studies

(1)

1.7 Chapter Summary

(3)

Chapter 2 The Jackknife

(12)

2.1 The Jackknife Estimator

(6)

2.2 Applications of Jackknifing in Biology

(5)

2.2.1 Single-Species Analyses

(1)

2.2.2 Genetics, Evolution, and Natural Selection

(1)

2.2.3 Community Ecology

(4)

2.3 Chapter Summary

(1)

Chapter 3 The Bootstrap

(40)

3.1 Resampling with Replacement

(1)

3.2 Standard Bootstrap Confidence Limits

(4)

3.3 Simple Percentile Confidence Limits

(6)

3.4 Bias-Corrected Percentile Confidence Limits

(5)

3.5 Accelerated Bias-Corrected Percentile Limits

(8)

3.6 Other Methods for Constructing Confidence Intervals

(3)

3.7 Transformations to Improve Bootstrap-t Intervals

(2)

3.8 Parametric Confidence Intervals

(1)

3.9 A Better Estimate of Bias

(1)

3.10 Bootstrap Tests of Significance

(3)

3.11 Balanced Bootstrap Sampling

(1)

3.12 Applications of Bootstrapping in Biology

(4)

3.12.1 Single-Species Ecology

(1)

3.12.2 Genetics, Evolution, and Natural Selection

(1)

3.12.3 Community Ecology

(1)

3.12.4 Other Ecological and Environmental Applications

(1)

3.13 Further Reading

(1)

3.14 Chapter Summary

(2)

Chapter 4 Monte Carlo Methods

(12)

4.1 Monte Carlo Tests

(3)

4.2 Generalized Monte Carlo Tests

(2)

4.3 Implicit Statistical Models

(2)

4.4 Applications of Monte Carlo Methods in Biology

(2)

4.4.1 Single-Species Ecology

(1)

4.4.2 Genetics and Evolution

(1)

4.4.3 Community Ecology

(1)

4.5 Chapter Summary

(3)

Chapter 5 Some General Considerations

(14)

5.1 Questions about Computer-Intensive Methods

(1)

5.2 Power

(1)

5.3 Number of Random Sets of Data Needed for a Test

(5)

5.4 Determining a Randomization Distribution Exactly

(2)

5.5 The Number of Replications for Confidence Intervals

101

(2)

5.6 More Efficient Bootstrap Sampling Methods

103

(1)

5.7 The Generation of Pseudo-Random Numbers

103

(1)

5.8 The Generation of Random Permutations

104

(1)

5.9 Chapter Summary

105

(2)

Chapter 6 One- and Two-Sample Tests

107

(28)

6.1 The Paired Comparisons Design

107

(5)

6.2 The One-Sample Randomization Test

112

(1)

6.3 The Two-Sample Randomization Test

113

(3)

6.4 Bootstrap Tests

116

(1)

6.5 Randomizing Residuals

117

(2)

6.6 Comparing the Variation in Two Samples

119

(3)

6.7 A Simulation Study

122

(2)

6.8 The Comparison of Two Samples on Multiple Measurements

124

(5)

6.9 Further Reading

129

(1)

6.10 Chapter Summary

130

(5)

Chapter 7 Analysis of Variance

135

(34)

7.1 One-Factor Analysis of Variance

135

(2)

7.2 Tests for Constant Variance

137

(1)

7.3 Testing for Mean Differences Using Residuals

138

(5)

7.4 Examples of More Complicated Types of Analysis of Variance

143

(18)

7.5 Procedures for Handling Unequal Variances

161

(1)

7.6 Other Aspects of Analysis of Variance

162

(1)

7.7 Further Reading

163

(2)

7.8 Chapter Summary

165

(4)

Chapter 8 Regression Analysis

169

(34)

8.1 Simple Linear Regression

169

(2)

8.2 Randomizing Residuals

171

(4)

8.3 Testing for a Nonzero β Value

175

(1)

8.4 Confidence Limits for β

175

(1)

8.5 Multiple Linear Regression

176

(4)

8.6 Alternative Randomization Methods with Multiple Regression

180

(16)

8.7 Bootstrapping and Jackknifing with Regression

196

(1)

8.8 Further Reading

197

(3)

8.9 Chapter Summary

200

(3)

Chapter 9 Distance Matrices and Spatial Data

203

(36)

9.1 Testing for Association between Distance Matrices

203

(2)

9.2 The Mantel Test

205

(2)

9.3 Sampling the Randomization Distribution

207

(3)

9.4 Confidence Limits for Regression Coefficients

210

(2)

9.5 The Multiple Mantel Test

212

(1)

9.6 Other Approaches with More Than Two Matrices

213

(17)

9.7 Further Reading

230

(2)

9.8 Chapter Summary

232

(7)

Chapter 10 Other Analyses on Spatial Data

239

(22)

10.1 Spatial Data Analysis

239

(1)

10.2 The Study of Spatial Point Patterns

239

(1)

10.3 Mead's Randomization Test

240

(5)

10.4 Tests for Randomness Based on Distances

245

(2)

10.5 Testing for an Association between Two Point Patterns

247

(1)

10.6 The Besag-Diggle Test

248

(2)

10.7 Tests Using Distances between Points

250

(2)

10.8 Testing for Random Marking

252

(3)

10.9 Further Reading

255

(1)

10.10 Chapter Summary

256

(5)

Chapter 11 Time Series

261

(40)

11.1 Randomization and Time Series

261

(1)

11.2 Randomization Tests for Serial Correlation

262

(5)

11.3 Randomization Tests for Trend

267

(7)

11.4 Randomization Tests for Periodicity

274

(7)

11.5 Irregularly Spaced Series

281

(2)

11.6 Tests on Times of Occurrence

283

(2)

11.7 Discussion on Procedures for Irregular Series

285

(5)

11.8 Bootstrap Methods

290

(1)

11.9 Monte Carlo Methods

290

(2)

11.10 Model-Based vs. Moving-Block Resampling

292

(2)

11.11 Further Reading

294

(3)

11.12 Chapter Summary

297

(4)

Chapter 12 Multivariate Data

301

(24)

12.1 Univariate and Multivariate Tests

301

(1)

12.2 Sample Mean Vectors and Covariance Matrices

301

(1)

12.3 Comparison of Sample Mean Vectors

302

(10)

12.4 Chi-Squared Analyses for Count Data

312

(2)

12.5 Comparison of Variations for Several Samples

314

(1)

12.6 Principal Components Analysis and Other One-Sample Methods

314

(3)

12.7 Discriminant Function Analysis

317

(3)

12.8 Further Reading

320

(1)

12.9 Chapter Summary

321

(4)

Chapter 13 Survival and Growth Data

325

(16)

13.1 Bootstrapping Survival Data

325

(2)

13.2 Bootstrapping for Variable Selection

327

(2)

13.3 Bootstrapping for Model Selection

329

(1)

13.4 Group Comparisons

330

(1)

13.5 Growth Data

331

(5)

13.6 Further Reading

336

(1)

13.7 Chapter Summary

337

(4)

Chapter 14 Nonstandard Situations

341

(30)

14.1 The Construction of Tests in Nonstandard Situations

341

(1)

14.2 Species Co-Occurrences on Islands

341

(10)

14.3 Alternative Switching Algorithms

351

(3)

14.4 Examining Time Changes in Niche Overlap

354

(6)

14.5 Probing Multivariate Data with Random Skewers

360

(5)

14.6 Ant Species Sizes in Europe

365

(5)

14.7 Chapter Summary

370

(1)

Chapter 15 Bayesian Methods

371

(10)

15.1 The Bayesian Approach to Data Analysis

371

(1)

15.2 The Gibbs Sampler and Related Methods

372

(5)

15.3 Biological Applications

377

(1)

15.4 Further Reading

378

(1)

15.5 Chapter Summary

379

(2)

Chapter 16 Final Comments

381

(4)

16.1 Randomization

381

(1)

16.2 Bootstrapping

382

(1)

16.3 Monte Carlo Methods in General

382

(1)

16.4 Classical vs. Bayesian Inference

383

(2)

References

385

(50)

Appendix Software for Computer-Intensive Statistics

435

(4)

Author Index

439

(10)

Subject Index

449

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

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Supplemental Materials