Models for Ecological Data

The environmental sciences are undergoing a revolution in the use of models and data. Facing ecological data sets of unprecedented size and complexity, environmental scientists are struggling to understand and exploit powerful new statistical tools for making sense of ecological processes.InModels for Ecological Data, James Clark introduces ecologists to these modern methods in modeling and computation. Assuming only basic courses in calculus and statistics, the text introduces readers to basic maximum likelihood and then works up to more advanced topics in Bayesian modeling and computation. Clark covers both classical statistical approaches and powerful new computational tools and describes how complexity can motivate a shift from classical to Bayesian methods. Through an available lab manual, the book introduces readers to the practical work of data modeling and computation in the language R. Based on a successful course at Duke University and National Science Foundation-funded institutes on hierarchical modeling,Models for Ecological Datawill enable ecologists and other environmental scientists to develop useful models that make sense of ecological data.Consistent treatment from classical to modern BayesUnderlying distribution theory to algorithm developmentMany examples and applicationsDoes not assume statistical backgroundExtensive supporting appendixesAccompanying lab manual in R

Preface	p. ix
Introduction	p. 1
Models in Context	p. 3
Complexity and Obscurity in Nature and in Models	p. 3
Making the Connections: Data, Inference, and Decision	p. 5
Two Elements of Models: Known and Unknown	p. 13
Learning with Models: Hypotheses and Quantification	p. 19
Estimation versus Forward Simulation	p. 23
Statistical Pragmatism	p. 24
Model Elements: Application to Population Growth	p. 27
A Model and Data Example	p. 27
Model State and Time	p. 30
Stochasticity for the Unknown	p. 42
Additional Background on Process Models	p. 44
Elements of Inference	p. 45
Point Estimation: Maximum Likelihood and the Method of Moments
Introduction	p. 47
Likelihood	p. 47
A Binomial Model	p. 53
Combining the Binomial and Exponential	p. 54
Maximum Likelihood Estimates for the Normal Distribution	p. 56
Population Growth	p. 57
Application: Fecundity	p. 60
Survival Analysis Using Maximum Likelihood	p. 62
Design Matrixes	p. 68
Numerical Methods for MLE	p. 71
Moment Matching	p. 71
Common Sampling Distributions and Dispersion	p. 74
Assumptions and Next Steps	p. 76
Elements of the Bayesian Approach	p. 77
The Bayesian Approach	p. 78
The Normal Distribution	p. 84
Subjective Probability and the Role of the Prior	p. 91
Confidence Envelopes and Prediction Intervals	p. 93
Classical Interval Estimation	p. 95
Bayesian Credible Intervals	p. 115
Likelihood Profile for Multiple Parameters	p. 120
Confidence Intervals for Several Parameters: Linear Regression	p. 122
Which Confidence Envelope to Use	p. 130
Predictive Intervals	p. 133
Uncertainty and Variability	p. 141
When Is It Bayesian?	p. 142
Model Assessment and Selection	p. 143
Using Statistics to Evaluate Models	p. 143
The Role of Hypothesis Tests	p. 144
Nested Models	p. 144
Additional Considerations for Classical Model Selection	p. 151
Bayesian Model Assessment	p. 154
Additional Thoughts on Bayesian Model Assessment	p. 159
Larger Models	p. 161
Computational Bayes: Introduction to Tools Simulation	p. 163
Simulation to Obtain the Posterior	p. 163
Some Basic Simulation Techniques	p. 164
Markov Chain Monte Carlo Simulation	p. 173
Application: Bayesian Analysis for Regression	p. 189
Using MCMC	p. 202
Computation for Bayesian Model Selection	p. 205
Priors on the Response	p. 209
The Basics Are Now Behind Us	p. 212
A Closer Look at Hierarchical Structures	p. 213
Hierarchical Models for Context	p. 213
Mixed and Generalized Linear Models	p. 216
Application: Growth Responses to CO2	p. 230
Thinking Conditionally	p. 235
Two Applications to Trees	p. 241
Noninformative Priors in Hierarchical Settings	p. 249
From Simple Models to Graphs	p. 249
More Advance Methods	p. 251
Time
Why Is Time Important?	p. 253
Time Series Terminology	p. 254
Descriptive Elements of Time Series Models	p. 255
The Frequency Domain	p. 264
Application: Detecting Density Dependence in Population Time Series	p. 264
Bayesian State Space Models	p. 272
Application: Black Noddy on Heron Island	p. 282
Nonlinear State Space Models	p. 289
Lags	p. 297
Regime Change	p. 298
Constraints on Time Series Data	p. 300
Additional Sources of Variablity	p. 301
Alternatives to the Gibbs Sampler	p. 302
More on Longitudinal Data Structures	p. 302
Intervention and Treatment Effects	p. 309
Capture-Recapture Studies	p. 318
Structured Models as Matrixes	p. 329
Structure as Systems of Difference Equations	p. 336
Time Series, Population Regulation, and Stochasticity	p. 347
Space-Time	p. 353
A Deterministic Model for a Stochastic Spa
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