Introduction to Bayesian methods in ecology and natural resources

✍ Scribed by Edwin James Green; William E. Strawderman; Andrew O. Finley

• Publisher: Springer
• Year: 2020
• Tongue: English
• Leaves: 188
• Category: Library

✦ Table of Contents

Contents
List of Code Boxes
1 Introduction
1.1 Bayesian and Non-Bayesian Inference
1.2 Bayes Theorem
1.3 Bayesian Inference
1.4 Pros and Cons of Bayesian Inference
References
2 Probability Theory and Some Useful Probability Distributions
2.1 Discrete and Continuous Random Variables
2.2 Expectation, Mean, Standard Deviation, and Variance
2.3 Unconditional, Conditional, Marginal, and Joint Distributions
2.4 Likelihood Functions and Random Samples
2.5 Some Useful Discrete Probability Distributions
2.5.1 Binomial Distribution
2.5.2 Multinomial Distribution
2.5.3 Poisson Distribution
2.6 Useful Continuous Distributions
2.6.1 Uniform Distribution
2.6.2 Normal Distribution
2.6.3 Multivariate Normal Distribution
2.6.4 t Distribution
2.6.5 Gamma Distribution
2.6.6 Wishart Distribution
2.6.7 Beta Distribution
2.6.8 Dirichlet Distribution
2.7 Exercises
References
3 Choice of Prior Distribution
3.1 Vague Prior Distributions
3.2 Improper Prior Distributions
3.3 Conjugate Prior Distributions
3.4 Prior Specification
3.4.1 Vague Priors
3.4.2 Informative Priors
3.4.3 Example: Poisson Sampling Model with Vague and Informative Priors
3.5 Exercises
References
4 Elementary Bayesian Analyses
4.1 Beta-Binomial Model
4.2 Normal Model, Known Variance
4.3 Normal Model, Unknown Variance
4.4 Hierarchical Models
4.4.1 Random and Fixed Effects
4.4.2 Exchangeability
4.4.3 Number of Levels in Hierarchical Models
4.5 Exercises
References
5 Hypothesis Testing and Model Choice
5.1 Examples
5.1.1 Deer Weights
5.1.2 Fire Scar Intervals
5.2 Hypothesis Testing Terminology
5.3 Error Types and Acceptance/Rejection of Hypotheses
5.4 Brief Philosophy of Hypothesis Testing
5.5 Model Choice
5.5.1 Within-Sample Versus Out-of-Sample Prediction
5.6 Bayes Factors
5.7 Information Theoretic Metrics
5.7.1 AIC
5.7.2 Bayesian Information Criterion
5.7.3 Deviance Information Criterion
5.7.4 Widely Applicable Information Criterion
5.7.5 Leave-One-Out Criterion
5.8 Credible Intervals
5.8.1 Point Null for Normal Mean, Variance Known
5.8.2 Point Null for Normal Mean, Variance Unknown
5.8.3 Testing Equality of Two Normal Means, Variances Unknown
5.9 Posterior Predictive Densities
5.9.1 Fire Scar Data
5.10 Exercises
References
6 Linear Models
6.1 Simple Linear Model: Trees Data
6.1.1 Predicting a New Observation
6.2 Hierarchical Linear Models
6.2.1 Rat Growth Data
6.2.2 Diet 2 Rats
6.2.3 Predicting a New Observation
6.2.4 Full Rat Data Set
6.3 Exercises
References
7 General Linear Models
7.1 Poisson Regression
7.1.1 Poisson Regression Example
7.2 Logistic Regression
7.2.1 Bernoulli Logistic Example
7.2.2 Binomial Logistic Example
7.3 Concluding Remarks
7.4 Exercises
References
8 Spatial Linear Models
8.1 Point-Referenced Spatial Models
8.1.1 Space-Varying Coefficient Models
8.1.2 Software
8.1.3 Tree Height-Diameter Data
8.2 Models for Large Spatial Data
8.3 Exercises
References
Appendix A Some Common Conjugate Models
Appendix B Markov Chain Monte Carlo Sampling
Appendix C Short Tutorial on OpenBUGS
C.1 Model Step
C.2 Data Step
C.3 Initial Values Step
C.4 A Few OpenBUGS ``Tricks''
C.5 Convergence
Appendix References