Table of Contents

Preface ix Acknowledgments xi 1. Introduction 1 1.1 Why Forecast? 1 1.2 The Informatics Challenge in Forecasting 3 1.3 The Model-Data Loop 4 1.4 Why Bayes? 6 1.5 Models as Scaffolds 7 1.6 Case Studies and Decision Support 8 1.7 Key Concepts 10 1.8 Hands-on Activities 10 2. From Models to Forecasts 11 2.1 The Traditional Modeler's Toolbox 11 2.2 Example: The Logistic Growth Model 12 2.3 Adding Sources of Uncertainty 14 2.4 Thinking Probabilistically 23 2.5 Predictability 25 2.6 Key Concepts 33 2.7 Hands-on Activities 33 3. Data, Large and Small 34 3.1 The Data Cycle and Best Practices 34 3.2 Data Standards and Metadata 38 3.3 Handling Big Data 40 3.4 Key Concepts 43 3.5 Hands-on Activities 43 4. Scientific Workflows and the Informatics of Model-Data Fusion 44 4.1 Transparency, Accountability, and Repeatability 44 4.2 Workflows and Automation 45 4.3 Best Practices for Scientific Computing 48 4.4 Key Concepts 51 4.5 Hands-on Activities 52 5. Introduction to Bayes 53 5.1 Confronting Models with Data 53 5.2 Probability 101 54 5.3 The Likelihood 56 5.4 Bayes' Theorem 61 5.5 Prior Information 65 5.6 Numerical Methods for Bayes 68 5.7 Evaluating MCMC Output 71 5.8 Key Concepts 74 5.9 Hands-on Activities 75 6. Characterizing Uncertainty 76 6.1 Non-Gaussian Error 76 6.2 Heteroskedasticity 82 6.3 Observation Error 83 6.4 Missing Data and Inverse Modeling 87 6.5 Hierarchical Models and Process Error 90 6.6 Autocorrelation 94 6.7 Key Concepts 96 6.8 Hands-on Activities 97 7. Case Study: Biodiversity, Populations, and Endangered Species 98 7.1 Endangered Species 98 7.2 Biodiversity 104 7.3 Key Concepts 106 7.4 Hands-on Activities 107 8. Latent Variables and State-Space Models 108 8.1 Latent Variables 108 8.2 State Space 110 8.3 Hidden Markov Time-Series Model 111 8.4 Beyond Time 114 8.5 Key Concepts 116 8.6 Hands-on Activities 117 9. Fusing Data Sources 118 9.1 Meta-analysis 120 9.2 Combining Data: Practice, Pitfalls, and Opportunities 123 9.3 Combining Data and Models across Space and Time 127 9.4 Key Concepts 130 9.5 Hands-on Activities 130 10. Case Study: Natural Resources 131 10.1 Fisheries 131 10.2 Case Study: Baltic Salmon 133 10.3 Key Concepts 137 11. Propagating, Analyzing, and Reducing Uncertainty 138 11.1 Sensitivity Analysis 138 11.2 Uncertainty Propagation 145 11.3 Uncertainty Analysis 155 11.4 Tools for Model-Data Feedbacks 158 11.5 Key Concepts 162 11.6 Hands-on Activities 163 Appendix A Properties of Means and Variances 163 Appendix B Common Variance Approximations 164 12. Case Study: Carbon Cycle 165 12.1 Carbon Cycle Uncertainties 165 12.2 State of the Science 166 12.3 Case Study: Model-Data Feedbacks 171 12.4 Key Concepts 174 12.5 Hands-on Activities 174 13. Data Assimilation 1: Analytical Methods 175 13.1 The Forecast Cycle 175 13.2 Kalman Filter 178 13.3 Extended Kalman Filter 183 13.4 Key Concepts 185 13.5 Hands-on Activities 186 14. Data Assimilation 2: Monte Carlo Methods 187 14.1 Ensemble Filters 187 14.2 Particle Filter 190 14.3 Model Averaging and Reversible Jump MCMC 194 14.4 Generalizing the Forecast Cycle 195 14.5 Key Concepts 197 14.6 Hands-on Activities 198 15. Epidemiology 199 15.1 Theory 200 15.2 Ecological Forecasting 201 15.3 Examples of Epidemiological Forecasting 202 15.4 Case Study: Influenza 205 15.5 Key Concepts 207 16. Assessing Model Performance 208 16.1 Visualization 208 16.2 Basic Model Diagnostics 211 16.3 Model Benchmarks 215 16.4 Data Mining the Residuals 217 16.5 Comparing Model Performance to Simple Statistics 217 16.6 Key Concepts 219 16.7 Hands-on Activities 219 17. Projection and Decision Support 221 17.1 Projections, Predictions, and Forecasting 222 17.2 Decision Support 223 17.3 Key Concepts 235 17.4 Hands-on Activities 236 18. Final Thoughts 237 18.1 Lessons Learned 237 18.2 Future Directions 240 References 245 Index 261

About the Author

Michael C. Dietze is associate professor in the Department of Earth and Environment at Boston University.

Reviews

"Shortlisted for the 2018 TWS Wildlife Publication Awards, The Wildlife Society"

"This book is unique in its scope, and it will be for many years, until ecologists embrace its message: to understand how nature works, we have to propose mechanistic models and test them. Their uncertainties reveal what we do not know, and where prediction error can be minimised by future work. . . . [This book] will give any reader a wider view of the data-model tandem, and dense information on how to step up to the next level of ecological forecasting."---Carsten F. Dormann, Basic and Applied Ecology

"[Dietze] does a great job of clearly explaining complex statistical procedures . . . . ecological modelers will find this book invaluable, and students who want to deepen their understanding of these topics will find it worthwhile."
*Conservation Biology*