Introduction to computer-intensive methods of data analysis in biology

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 9
What are computer-intensive data methods?......Page 11
Why computer-intensive methods?......Page 12
Why S-PLUS?......Page 17
Further reading......Page 18
Introduction......Page 19
Why the mean?......Page 20
Nuisance parameters don’t always disappear......Page 23
Why we use least squares so much......Page 24
More on least squares......Page 26
Generalizing the MLE approach in relation to least squares estimation......Page 29
Multiple likelihoods: estimating heritability using the binomial and MLE......Page 30
Logistic regression: connecting the binomial with regression......Page 33
From binomial to multinomial......Page 35
Combining simulation and MLE to estimate population parameters......Page 36
Method 1: an exhaustive approach......Page 38
Method 2: the log-likelihood ratio approach......Page 39
Method 3: a standard error approach......Page 40
Testing model fit......Page 42
Comparing models......Page 44
Summary......Page 47
Exercises......Page 48
List of symbols used in Chapter 2......Page 50
Point estimation......Page 52
Hypothesis testing......Page 53
The jackknife of the mean......Page 54
Variance components......Page 55
The estimation of ratios: variances and covariances......Page 62
The estimation of ratios: ecological indices......Page 64
The estimation of ratios: population parameters......Page 65
Estimating ratios or products from two separate samples......Page 67
Estimating parameters of nonlinear models......Page 68
Checking the jackknife by bootstrapping the data......Page 70
Summary......Page 72
Exercises......Page 73
List of symbols used in Chapter 3......Page 74
Introduction......Page 76
Bias-adjusted bootstrap estimate......Page 77
Method 1: standard error approach......Page 78
Method 2: first percentile method......Page 79
Method 4: bias-corrected percentile method......Page 80
Method 5: accelerated bias-corrected percentile method......Page 82
Method 6: percentile-t-method......Page 83
Hypothesis testing......Page 84
Bootstrapping the mean......Page 85
Bootstrapping the variance......Page 87
More on sample size and confidence intervals: the Gini coefficient......Page 88
Yet more on sample size and the bootstrap: not all bootstraps are created equal......Page 89
The bootstrap can produce confidence limits that are too large: an example from niche overlap......Page 90
Bootstrapping when the unit is not the individual observation......Page 92
Bootstrapping to estimate several parameters: linear regression......Page 94
Bootstrapping to estimate several parameters: nonlinear regression......Page 97
The bootstrap as a hypothesis testing method......Page 99
Bootstrapping phylogenies: the problem of deciding what a bootstrap actually measures......Page 103
Summary......Page 107
Exercises......Page 108
List of symbols used in Chapter 4......Page 110
Introduction......Page 112
An illustration of the approach: testing the difference between two means......Page 113
How many samples are required?......Page 115
Method 1: estimating the standard error from the randomization procedure......Page 116
Method 3: average percentile method......Page 121
Single-factor (one-way) analysis of variance......Page 122
Analysis of variance and the question of how to randomize......Page 128
The question of balance......Page 131
More on homogeneity: the x2 test......Page 134
Linear and multiple regression: dealing with non-normal errors......Page 138
Correlation and regression: dealing with the problem of non-independence......Page 140
Comparing distance matrices: the Mantel test......Page 144
Comparing matrices: other tests......Page 146
Testing for density-dependence......Page 149
Monte Carlo methods: two illustrative examples......Page 150
Validating step-wise regression......Page 152
Generalized Monte Carlo significance tests......Page 153
Patterns of species co-occurrences......Page 157
Size structure and community organization......Page 159
Summary......Page 161
Further reading......Page 162
Exercises......Page 163
List of symbols used in Chapter 5......Page 166
Introduction......Page 167
The problem of multiple, contending models......Page 168
Cross-validation......Page 171
One predictor variable......Page 172
Locally weighted regression smoothing......Page 174
The cubic spline......Page 179
Two predictor variables......Page 181
One predictor variable......Page 184
Several predictor variables......Page 186
How to split......Page 189
Tree pruning: the cost-complexity measure......Page 198
Tree pruning: cross-validation......Page 199
Tree pruning and testing: a randomization approach......Page 200
Putting it all together: the extinction of the avifauna of New Zealand......Page 202
Summary......Page 206
Exercises......Page 208
List of symbols used in Chapter 6......Page 212
Introduction......Page 214
Derivation of Bayes’ theorem......Page 215
A simple classification problem......Page 216
Estimating the mean of a normal distribution......Page 218
Natural conjugate priors......Page 219
Naïve Informative......Page 221
Hierarchical Bayesian......Page 223
Effects of different priors: the difference between two means......Page 224
Sequential Bayes’ estimation: survival estimates......Page 228
An application of sequential Bayes’ estimation: population estimation using mark-recapture......Page 229
Empirical Bayes’ estimation: the James–Stein estimator of the mean......Page 232
Predictive distributions: the estimation of parasitism rate in cowbirds......Page 234
Hypothesis testing in a Bayesian framework: the probability of extinction from sighting data......Page 236
Summary......Page 239
Exercises......Page 240
List of symbols used in Chapter 7......Page 241
References......Page 243
Data frames......Page 252
Lists......Page 253
Some examples......Page 254
Manipulating data......Page 256
Appendix B: Brief description of S-PLUS subroutines used in this book......Page 259
C.2.1 Calculating parameter values for a threshold model......Page 263
C.2.2 Estimation of parameters of a simple logistic curve......Page 264
C.2.3 Locating lower and upper confidence limits for heritability of a threshold trait given offspring data......Page 265
C.2.4 95% confidence interval for parameters Lmax and k of the von Bertalanffy equation conditioned on t0 and variance......Page 266
C.2.5 Output from S-PLUS for von Bertalanffy model fit using dialog box......Page 267
C.2.7 Comparing a 3-parameter with 2-parameter von Bertalanffy model using nlmin routine......Page 268
C.2.8 Comparing one (= constant proportion) and two parameter logistic model......Page 269
C.2.9 Comparing two von Bertalanffy growth curves (males and females) using nlmin function......Page 272
C.2.10 Comparing two von Bertalanffy growth curves (males and females) using nls function......Page 273
Alternative coding using the anova function to compare models (results are identical)......Page 274
C.2.11 Comparing von Bertalanffy growth curves with respect to theta-3(=t0) assuming differences between the sexes in other parameters......Page 275
C.3.1 An analysis of the Jackknife analysis of the variance 100 replicated data sets of 10 random normal, N(0,1), observations per data set......Page 276
C.3.2 Testing for differences between the variances of two data sets using the jackknife......Page 277
C.3.3 Estimating the pseudovalues for the genetic variance – covariance matrix for full-sib data......Page 278
C.3.4 Simulating data sets in which two characters are inherited according to a quantitative genetic algorithm......Page 281
C.3.5 Coding to estimate heritability for a full sib design using the routine “jackknife”......Page 282
C.3.6 Generation of data following the von Bertalanffy function......Page 283
C.3.7 Jackknife estimation of parameter values for von Bertalanffy data generated by coding shown in C.3.6......Page 284
C.3.8 Analysis of parameter estimation of the von Bertalanffy function using the jackknife and MLE methods......Page 285
Random generation using bootstrap approach. Suppose the observed data are in file Data......Page 287
C.4.1 Coding to generate 30 random normal values, generate 1000 bootstrap values and determine basic statistics......Page 288
C.4.2 Coding to generate 500 samples of size 30 from N(0,1) to test bootstrap method of estimating the mean......Page 289
C.4.3 Coding to bootstrap the Gini coefficient of inequality......Page 290
C.4.4 Coding to generate data for linear regression with normal or gamma distribution of errors and estimate parameters using least squares, jackknife, and bootstrap......Page 291
C.4.5 Coding to simulate 1000 linear regression data sets, analyze by least squares and test for 95% coverage......Page 293
C.4.6 Coding to generate von Bertalanffy growth data and fit model by bootstrapping least squares estimates of parameters......Page 295
C.4.7 Coding to generate multiple samples of the von Bertalanffy growth function and fit by bootstrap......Page 296
Coding to analyze Data.txt......Page 297
C.5.1 A randomization test of a difference between two means......Page 298
C.5.3 Estimation of the required sample size for a randomization test of a difference between two means......Page 299
C.5.4 Estimation of the probabilities for differing values of High and Low for the jackal data. See Figure 5.2 for output......Page 300
C.5.5 Estimation of the standard error, SE, using three approximate methods......Page 301
C.5.6 Randomization of one-way analysis of variance of ant consumption data......Page 303
C.5.7 Randomization of one-way analysis of variance using “by” routine of S-PLUS......Page 304
C.5.8 Randomization testing a two-way analysis of variance......Page 305
C.5.9 Levene\'s test for homogeneity of variances......Page 306
C.5.10 x2 contingency analysis by randomization......Page 307
C.5.11 Randomization analysis of intercept and slope in linear regression on generated data......Page 309
C.5.12 Coding to create distance and difference matrices shown in Figure 5.12......Page 310
C.5.13 The Mantel Test......Page 311
C.6.1 Cross-validation of two multiple regression equations using 10% of the data set as the test set......Page 312
C.6.2 Coding to fit a smoothed function using the loess routine. Coding to generate plots given but output not shown......Page 313
C.6.3 Coding for 10-fold cross-validation of loess fit......Page 314
C.6.4 Coding to fit loess curve to multivariate data......Page 315
C.6.5 Comparison of two fitted loess surfaces using density data......Page 316
C.6.6 Coding to produce plots and fitted curves to the Chapman equation shown in Figure 6.7 with testing of fits. Text output but not plots shown......Page 318
C.6.7 Coding to generate regression tree and perform cross-validation......Page 320
C.6.8 Function to perform randomization test of a given regression tree......Page 321
C.7.1 Calculation of posterior probabilities for a normal mean based on prior distributions of the mean and variance and a single observation, x......Page 323
C.7.2 Bayesian analysis of binomial data......Page 324
C.7.3 Sequential Bayesian analysis of mark-recapture data......Page 325
Question 2.1......Page 326
Question 2.4......Page 327
Question 2.5......Page 328
Question 2.7......Page 329
Question 2.8......Page 330
Question 2.10......Page 331
Question 2.11......Page 332
Question 3.1......Page 333
Question 3.2......Page 334
Alternative coding using jackknife routine......Page 335
Question 3.3......Page 336
Question 3.4......Page 338
Question 3.5......Page 339
Question 3.6......Page 341
Question 4.1......Page 343
Question 4.2......Page 344
Question 4.3......Page 346
Question 4.5......Page 347
Question 4.6......Page 348
Question 4.7......Page 349
Question 4.8......Page 350
Question 5.1......Page 352
Question 5.2......Page 353
Question 5.3......Page 354
Question 5.4......Page 355
Question 5.5......Page 356
Question 5.7......Page 357
Question 5.8......Page 358
Question 6.1......Page 359
Question 6.2......Page 360
Question 6.3......Page 361
Question 6.4......Page 362
Question 6.5......Page 364
Question 6.7......Page 366
Question 6.8......Page 368
Question 6.9......Page 369
Question 7.2......Page 372
Question 7.3......Page 373
Question 7.4......Page 374
Index......Page 375