Statistical Computation for Environmental Sciences in R

Preface ixPart I. Introduction 1Chapter 1: Models in Context 31.1 Complexity and Obscurity in Nature and in Models 31.2 Making the Connections: Data, Inference, and Decision 51.3 Two Elements of Models: Known and Unknown 131.4 Learning with Models: Hypotheses and Quantification 191.5 Estimation versus Forward Simulation 231.6 Statistical Pragmatism 24Chapter 2: Model Elements: Application to Population Growth 272.1 A Model and Data Example 272.2 Model State and Time 302.3 Stochasticity for the Unknown 422.4 Additional Background on Process Models 44Part II. Elements of Inference 45Chapter 3: Point Estimation: Maximum Likelihood and the Method of Moments3.1 Introduction 473.2 Likelihood 473.3 A Binomial Model 533.4 Combining the Binomial and Exponential 543.5 Maximum Likelihood Estimates for the Normal Distribution 563.6 Population Growth 573.7 Application: Fecundity 603.8 Survival Analysis Using Maximum Likelihood 623.9 Design Matrixes 683.10 Numerical Methods for MLE 713.11 Moment Matching 713.12 Common Sampling Distributions and Dispersion 743.13 Assumptions and Next Steps 76Chapter 4: Elements of the Bayesian Approach 774.1 The Bayesian Approach 784.2 The Normal Distribution 844.3 Subjective Probability and the Role of the Prior 91Chapter 5: Confidence Envelopes and Prediction Intervals 935.1 Classical Interval Estimation 955.2 Bayesian Credible Intervals 1155.3 Likelihood Profile for Multiple Parameters 1205.4 Confidence Intervals for Several Parameters: Linear Regression 1225.5 Which Confidence Envelope to Use 1305.6 Predictive Intervals 1335.7 Uncertainty and Variability 1415.8 When Is It Bayesian? 142Chapter 6: Model Assessment and Selection 1436.1 Using Statistics to Evaluate Models 1436.2 The Role of Hypothesis Tests 1446.3 Nested Models 1446.4 Additional Considerations for Classical Model Selection 1516.5 Bayesian Model Assessment 1546.6 Additional Thoughts on Bayesian Model Assessment 159Part III. Larger Models 161Chapter 7: Computational Bayes: Introduction to Tools Simulation 1637.1 Simulation to Obtain the Posterior 1637.2 Some Basic Simulation Techniques 1647.3 Markov Chain Monte Carlo Simulation 1737.4 Application: Bayesian Analysis for Regression 1897.5 Using MCMC 2027.6 Computation for Bayesian Model Selection 2057.7 Priors on the Response 2097.8 The Basics Are Now Behind Us 212Chapter 8: A Closer Look at Hierarchical Structures 2138.1 Hierarchical Models for Context 2138.2 Mixed and Generalized Linear Models 2168.3 Application: Growth Responses to CO2 2308.4 Thinking Conditionally 2358.5 Two Applications to Trees 2418.6 Noninformative Priors in Hierarchical Settings 2498.7 From Simple Models to Graphs 249Part IV. More Advance Methods 251Chapter 9: Time9.1 Why Is Time Important? 2539.2 Time Series Terminology 2549.3 Descriptive Elements of Time Series Models 2559.4 The Frequency Domain 2649.5 Application: Detecting Density Dependence in Population Time Series 2649.6 Bayesian State Space Models 2729.7 Application: Black Noddy on Heron Island 2829.8 Nonlinear State Space Models 2899.9 Lags 2979.10 Regime Change 2989.11 Constraints on Time Series Data 3009.12 Additional Sources of Variablity 3019.13 Alternatives to the Gibbs Sampler 3029.14 More on Longitudinal Data Structures 3029.15 Intervention and Treatment Effects 3099.16 Capture-Recapture Studies 3189.17 Structured Models as Matrixes 3299.18 Structure as Systems of Difference Equations 3369.19 Time Series, Population Regulation, and Stochasticity 347Chapter 10: Space-Time 35310.1 A Deterministic Model for a Stochastic Spatial Process 35410.2 Classical Inference on Population Movement 35910.3 Island Biogeography and Metapopulations 37810.4 Estimation of Passive Dispersal 38810.5 A Bayesian Framework 39710.6 Models for Explicit Space 40110.7 Point-Referenced Data 40310.8 Block-Referenced Data and Misalignment 41210.9 Hierarchical Treatment of Space 41510.10 Application: A Spatio-Temporal Model of Population Spread 42410.11 How to Handle Space 432Chapter 11: Some Concluding Perspectives 43511.1 Models, Data, and Decision 43511.2 The Promise of Graphical Models, Improved Algorithms, and Faster Computers 43711.3 Predictions and What to Do with Them 44411.4 Some Remarks on Software 456Appendix A Taylor Series 457Appendix B Some Notes on Differential and Difference Equations 464Appendix C Basic Matrix Algebra 486Appendix D Probability Models 502Appendix E Basic Life History Calculations 541Appendix F Common Distributions 573Appendix G Common Conjugate Likelihood-Prior Pairs 583References 585Index 615