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

by Manly; Bryan F.J.

• ISBN13: 9781584885412
• ISBN10: 1584885416
• Edition: 3rd
• Format: Hardcover
• Copyright: 2006-08-15
• Publisher: Chapman & Hall/

Summary

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.

Table of Contents

Chapter 1 Randomization	1	(28)
1.1 The Idea of a Randomization Test	1	(3)
1.2 Examples of Randomization Tests	4	(10)
1.3 Aspects of Randomization Testing Raised by the Examples	14	(4)
1.3.1 Sampling the Randomization Distribution or Systematic Enumeration	15	(1)
1.3.2 Equivalent Test Statistics	16	(1)
1.3.3 Significance Levels for Classical and Randomization Tests	17	(1)
1.3.4 Limitations of Randomization Tests	18	(1)
1.4 Confidence Limits by Randomization	18	(3)
1.5 Applications of Randomization in Biology and Related Areas	21	(4)
1.5.1 Single Species Ecology	21	(1)
1.5.2 Genetics, Evolution, and Natural Selection	22	(1)
1.5.3 Community Ecology	23	(2)
1.5.4 Other Environmental Applications	25	(1)
1.6 Randomization and Observational Studies	25	(1)
1.7 Chapter Summary	26	(3)
Chapter 2 The Jackknife	29	(12)
2.1 The Jackknife Estimator	29	(6)
2.2 Applications of Jackknifing in Biology	35	(5)
2.2.1 Single-Species Analyses	35	(1)
2.2.2 Genetics, Evolution, and Natural Selection	35	(1)
2.2.3 Community Ecology	36	(4)
2.3 Chapter Summary	40	(1)
Chapter 3 The Bootstrap	41	(40)
3.1 Resampling with Replacement	41	(1)
3.2 Standard Bootstrap Confidence Limits	42	(4)
3.3 Simple Percentile Confidence Limits	46	(6)
3.4 Bias-Corrected Percentile Confidence Limits	52	(5)
3.5 Accelerated Bias-Corrected Percentile Limits	57	(8)
3.6 Other Methods for Constructing Confidence Intervals	65	(3)
3.7 Transformations to Improve Bootstrap-t Intervals	68	(2)
3.8 Parametric Confidence Intervals	70	(1)
3.9 A Better Estimate of Bias	70	(1)
3.10 Bootstrap Tests of Significance	71	(3)
3.11 Balanced Bootstrap Sampling	74	(1)
3.12 Applications of Bootstrapping in Biology	74	(4)
3.12.1 Single-Species Ecology	75	(1)
3.12.2 Genetics, Evolution, and Natural Selection	76	(1)
3.12.3 Community Ecology	77	(1)
3.12.4 Other Ecological and Environmental Applications	77	(1)
3.13 Further Reading	78	(1)
3.14 Chapter Summary	79	(2)
Chapter 4 Monte Carlo Methods	81	(12)
4.1 Monte Carlo Tests	81	(3)
4.2 Generalized Monte Carlo Tests	84	(2)
4.3 Implicit Statistical Models	86	(2)
4.4 Applications of Monte Carlo Methods in Biology	88	(2)
4.4.1 Single-Species Ecology	89	(1)
4.4.2 Genetics and Evolution	89	(1)
4.4.3 Community Ecology	90	(1)
4.5 Chapter Summary	90	(3)
Chapter 5 Some General Considerations	93	(14)
5.1 Questions about Computer-Intensive Methods	93	(1)
5.2 Power	94	(1)
5.3 Number of Random Sets of Data Needed for a Test	94	(5)
5.4 Determining a Randomization Distribution Exactly	99	(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