Bayesian Data Analysis in Ecology Using Linear Models with R, BUGS, and Stan

Bayesian Data Analysis in Ecology Using Linear Models with R, BUGS, and STAN examines the Bayesian and frequentist methods of conducting data analyses. The book provides the theoretical background in an easy-to-understand approach, encouraging readers to examine the processes that generated their data. Including discussions of model selection, model checking, and multi-model inference, the book also uses effect plots that allow a natural interpretation of data.

Bayesian Data Analysis in Ecology Using Linear Models with R, BUGS, and STAN introduces Bayesian software, using R for the simple modes, and flexible Bayesian software (BUGS and Stan) for the more complicated ones. Guiding the ready from easy toward more complex (real) data analyses ina step-by-step manner, the book presents problems and solutions—including all R codes—that are most often applicable to other data and questions, making it an invaluable resource for analyzing a variety of data types.

• Introduces Bayesian data analysis, allowing users to obtain uncertainty measurements easily for any derived parameter of interest
• Written in a step-by-step approach that allows for eased understanding by non-statisticians
• Includes a companion website containing R-code to help users conduct Bayesian data analyses on their own data
• All example data as well as additional functions are provided in the R-package blmeco

Graduate students and professionals in ecology, biogeography, and biology

• Digital Assets
• Acknowledgments
• Chapter 1. Why do we Need Statistical Models and What is this Book About?
  • 1.1. Why We Need Statistical Models
  • 1.2. What This Book is About
• Chapter 2. Prerequisites and Vocabulary
  • 2.1. Software
  • 2.2. Important Statistical Terms and How to Handle Them in R
• Chapter 3. The Bayesian and the Frequentist Ways of Analyzing Data
  • 3.1. Short Historical Overview
  • 3.2. The Bayesian Way
  • 3.3. The Frequentist Way
  • 3.4. Comparison of the Bayesian and the Frequentist Ways
• Chapter 4. Normal Linear Models
  • 4.1. Linear Regression
  • 4.2. Regression Variants: ANOVA, ANCOVA, and Multiple Regression
• Chapter 5. Likelihood
  • 5.1. Theory
  • 5.2. The Maximum Likelihood Method
  • 5.3. The Log Pointwise Predictive Density
• Chapter 6. Assessing Model Assumptions: Residual Analysis
  • 6.1. Model Assumptions
  • 6.2. Independent and Identically Distributed
  • 6.3. The QQ Plot
  • 6.4. Temporal Autocorrelation
  • 6.5. Spatial Autocorrelation
  • 6.6. Heteroscedasticity
• Chapter 7. Linear Mixed Effects Models
  • 7.1. Background
  • 7.2. Fitting a Linear Mixed Model in R
  • 7.3. Restricted Maximum Likelihood Estimation
  • 7.4. Assessing Model Assumptions
  • 7.5. Drawing Conclusions
  • 7.6. Frequentist Results
  • 7.7. Random Intercept and Random Slope
  • 7.8. Nested and Crossed Random Effects
  • 7.9. Model Selection in Mixed Models
• Chapter 8. Generalized Linear Models
  • 8.1. Background
  • 8.2. Binomial Model
  • 8.3. Fitting a Binary Logistic Regression in R
  • 8.4. Poisson Model
• Chapter 9. Generalized Linear Mixed Models
  • 9.1. Binomial Mixed Model
  • 9.2. Poisson Mixed Model
• Chapter 10. Posterior Predictive Model Checking and Proportion of Explained Variance
  • 10.1. Posterior Predictive Model Checking
  • 10.2. Measures of Explained Variance
• Chapter 11. Model Selection and Multimodel Inference
  • 11.1. When and Why We Select Models and Why This is Difficult
  • 11.2. Methods for Model Selection and Model Comparisons
  • 11.3. Multimodel Inference
  • 11.4. Which Method to Choose and Which Strategy to Follow
• Chapter 12. Markov Chain Monte Carlo Simulation
  • 12.1. Background
  • 12.2. MCMC Using BUGS
  • 12.3. MCMC Using Stan
  • 12.4. Sim, BUGS, and Stan
• Chapter 13. Modeling Spatial Data Using GLMM
  • 13.1. Background
  • 13.2. Modeling Assumptions
  • 13.3. Explicit Modeling of Spatial Autocorrelation
• Chapter 14. Advanced Ecological Models
  • 14.1. Hierarchical Multinomial Model to Analyze Habitat Selection Using BUGS
  • 14.2. Zero-Inflated Poisson Mixed Model for Analyzing Breeding Success Using Stan
  • 14.3. Occupancy Model to Measure Species Distribution Using Stan
  • 14.4. Territory Occupancy Model to Estimate Survival Using BUGS
  • 14.5. Analyzing Survival Based on Mark-Recapture Data Using Stan
• Chapter 15. Prior Influence and Parameter Estimability
  • 15.1. How to Specify Prior Distributions
  • 15.2. Prior Sensitivity Analysis
  • 15.3. Parameter Estimability
• Chapter 16. Checklist
  • 16.1. Data Analysis Step by Step
• Chapter 17. What Should I Report in a Paper
  • 17.1. How to Present the Results
  • 17.2. How to Write Up the Statistical Methods
• References
• Index