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| Acknowledgments | |
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| Introduction and Background | |
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| Introduction | |
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| What This Book Is Not About | |
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| Frameworks for Modeling | |
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| Frameworks for Statistical Inference | |
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| Frameworks for Computing | |
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| Outline of the Modeling Process | |
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| R Supplement | |
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| Exploratory Data Analysis and Graphics | |
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| Introduction | |
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| Getting Data into R | |
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| Data Types | |
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| Exploratory Data Analysis and Graphics | |
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| Conclusion | |
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| R Supplement | |
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| Deterministic Functions for Ecological Modeling | |
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| Introduction | |
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| Finding Out about Functions Numerically | |
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| Finding Out about Functions Analytically | |
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| Bestiary of Functions | |
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| Conclusion | |
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| R Supplement | |
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| Probability and Stochastic Distributions for Ecological Modeling | |
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| Introduction: Why Does Variability Matter? | |
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| Basic Probability Theory | |
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| Bayes' Rule | |
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| |
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| Analyzing Probability Distributions | |
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| |
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| Bestiary of Distributions | |
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| |
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| Extending Simple Distributions: Compounding and Generalizing | |
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| |
| R Supplement | |
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| |
| Stochastic Simulation and Power Analysis | |
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| |
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| Introduction | |
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| Stochastic Simulation | |
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| Power Analysis | |
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| Likelihood and All That | |
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| Introduction | |
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| Parameter Estimation: Single Distributions | |
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| Estimation for More Complex Functions | |
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| Likelihood Surfaces, Profiles, and Confidence Intervals | |
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| Confidence Intervals for Complex Models: Quadratic Approximation | |
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| Comparing Models | |
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| Conclusion | |
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| Optimization and All That | |
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| Introduction | |
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| Fitting Methods | |
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| Markov Chain Monte Carlo | |
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| Fitting Challenges | |
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| Estimating Confidence Limits of Functions of Parameters | |
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| R Supplement | |
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| Likelihood Examples | |
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| Tadpole Predation | |
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| Goby Survival | |
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| Seed Removal | |
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| Standard Statistics Revisited | |
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| Introduction | |
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| General Linear Models | |
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| Nonlinearity: Nonlinear Least Squares | |
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| Nonnormal Errors: Generalized Linear Models | |
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| R Supplement | |
| |
| |
| |
| Modeling Variance | |
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| |
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| Introduction | |
| |
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| Changing Variance within Blocks | |
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| Correlations: Time-Series and Spatial Data | |
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| Multilevel Models: Special Cases | |
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| General Multilevel Models | |
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| Challenges | |
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| Conclusion | |
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| R Supplement | |
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| Dynamic Models | |
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| Introduction | |
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| Simulating Dynamic Models | |
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| Observation and Process Error | |
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| Process and Observation Error | |
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| SIMEX | |
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| State-Space Models | |
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| Conclusions | |
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| R Supplement | |
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| Afterword | |
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| Algebra and Calculus Basics | |
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| Exponentials and Logarithms | |
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| Differential Calculus | |
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| |
| Partial Differentiation | |
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| |
| Integral Calculus | |
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| |
| Factorials and the Gamma Function | |
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| Probability | |
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| |
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| The Delta Method | |
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| Linear Algebra Basics | |
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| Bibliography | |
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| |
| Index of R Arguments, Functions, and Packages | |
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| General Index | |