Bayesian Applications in Environmental and Ecological Studies with R and Stan

✍ Scribed by Song S. Qian, Mark R. DuFour, Ibrahim Alameddine

• Publisher: CRC Press/Chapman & Hall
• Year: 2022
• Tongue: English
• Leaves: 416
• Series: Chapman & Hall/CRC Applied Environmental Series
• Category: Library

✦ Synopsis

Modern ecological and environmental sciences are dominated by observational data. As a result, traditional statistical training often leaves scientists ill-prepared for the data analysis tasks they encounter in their work. Bayesian methods provide a more robust and flexible tool for data analysis, as they enable information from different sources to be brought into the modelling process. Bayesian Applications in Evnironmental and Ecological Studies with R and Stan provides a Bayesian framework for model formulation, parameter estimation, and model evaluation in the context of analyzing environmental and ecological data.

Features
• An accessible overview of Bayesian methods in environmental and ecological studies
• Emphasizes the hypothetical deductive process, particularly model formulation
• Necessary background material on Bayesian inference and Monte Carlo simulation
• Detailed case studies, covering water quality monitoring and assessment, ecosystem response to urbanization, fisheries ecology, and more
• Advanced chapter on Bayesian applications, including Bayesian networks and a change point model
• Complete code for all examples, along with the data used in the book, are available via GitHub

The book is primarily aimed at graduate students and researchers in the environmental and ecological sciences, as well as environmental management professionals. This is a group of people representing diverse subject matter fields, who could benefit from the potential power and flexibility of Bayesian methods.

✦ Table of Contents

Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Contents
Foreword
Preface
Acknowledgments
1. Overview
1.1. Two Modes of Reasoning: Deduction vs. Induction
1.1.1. Testing for Snake Fungal Disease
1.2. Bayesian versus Classical Statistics
1.3. Guiding Principles
1.4. Examples
1.4.1. Gill-net Monitoring Data
1.4.2. Effects of Urbanization on Stream Ecosystems
1.4.3. Everglades Studies
1.4.4. Compliance Assessment under the U.S. Clean Water Act
1.5. Summary
2. Bayesian Inference and Monte Carlo Simulation
2.1. The Role of Simulation in Statistics
2.2. Bayesian Monte Carlo
2.3. Sampling from Known Distributions
2.3.1. Inverse-CDF Methods
2.3.2. Acceptance-Rejection Methods
2.3.3. Relationships Method
2.3.4. Numeric Integration
2.3.5. A Statistical Estimation Example
2.4. Markov Chain Monte Carlo Simulation
2.4.1. Metropolis-Hastings Algorithm
2.4.2. Gibbs Sampler
2.4.2.1. Examples
2.5. Bayesian Inference Using Markov Chain Monte Carlo
2.5.1. Metropolis-Hastings within a Gibbs Sampler
2.6. MCMC Software
2.6.1. Stan
2.7. Summary
3. An Overview of Bayesian Inference
3.1. The General Approach
3.2. Example: Assessing Water Quality Standard Compliance in the Neuse River Estuary
3.2.1. Background
3.2.2. Study Area and Data
3.2.3. The Problem of Specification
3.2.4. The Problem of Estimation and Distribution
3.2.4.1. The Likelihood Function and Prior Distribution
3.2.4.2. Deriving the Posterior Distribution
3.2.4.3. Predictive Distribution
3.2.5. Application in the Neuse River Estuary
3.3. Specifying Prior Distributions
3.4. Summary
4. Environmental Monitoring and Assessment – Normal Response Models
4.1. A Simulation-Based Inference
4.1.1. Using Stan through R Package rstan
4.2. Examples of Analysis of Variance
4.2.1. The Seaweed Grazer Example
4.2.2. The Gulf of Mexico Hypoxia Example
4.2.2.1. Study Background
4.2.2.2. Prior Analysis
4.2.2.3. Implementation in Stan and Alternative Models
4.3. Regression Models
4.3.1. Linear Regression Example
4.3.2. Nonlinear Regression Models
4.3.2.1. Calibration-Curve Methods
4.3.2.2. The Toledo Water Crisis of 2014
4.3.2.3. ELISA Test Data
4.3.2.4. Alternative Parameterization
4.4. Fitting a Hierarchical Model Sequentially
4.5. A Mixture of Two Normal Distributions
4.5.1. Estimating Background Contaminant Concentrations
4.6. Summary
5. Population and Community: Count Variables
5.1. Poisson and Negative Binomial Distributions
5.2. Analysis of Variance/Deviance
5.2.1. The Liverpool Moth Example
5.2.2. The Seedling Recruitment Example
5.2.2.1. The Classical Generalized Linear Models
5.2.2.2. Bayesian Implementation of GLM
5.2.2.3. Over-dispersion
5.2.2.4. Spatial Auto-correlation
5.3. Imperfect Detection
5.3.1. The Data Augmentation Algorithm
5.3.2. Example: COVID-19 Testing in Ohio, USA
5.3.2.1. Initial Testing
5.3.2.2. Shelter in Place and Reopening
5.3.2.3. Programming Notes
5.3.3. Zero-Inflation
5.3.3.1. Example: Simulated Data and ZIP Model
5.3.3.2. Example: Seabird By-Catch Data
5.3.3.3. Example: Estimating Sturgeon Population Trends
5.3.3.4. Example: Effects of Urbanization on Stream Ecosystems
5.4. Multinomial Count Data
5.4.1. The Insect Oviposition Example
5.4.2. The EUSE Example – Multinomial Logistic Regression
5.4.3. The Everglades Example – A Missing Data Problem
5.5. Summary
6. Hierarchical Modeling and Aggregation
6.1. Aggregation in Science and Management
6.2. Subjective Ignorance and Objective Knowledge
6.3. Stein's Paradox and Bayesian Hierarchical Model
6.4. Examples
6.4.1. Example 1: Setting Environmental Standards in the Everglades
6.4.2. Example 2: Environmental Standard Compliance
6.4.3. Example 3: Multilevel Modeling with Group-Level Predictors
6.4.4. Example 4: Multilevel Modeling for Evaluating Fisheries Sampling Methods
6.4.4.1. Regional Differences in Gill-net Catchability
6.4.4.2. Species-length relationships
6.4.5. Censored Data and Imperfect Detection
6.4.5.1. Example 5: Drinking Water Safety Review in the US
6.4.5.2. Example 6: Water Quality Survey of China's Drinking Water Sources
6.4.5.3. Example 7: Developing a Drinking Water Regulatory Standard in the U.S.
6.5. When Data from Nonexchangeable Units Are Mixed
6.5.1. Example 8: Are Small Wetlands More Effective in Nutrient Retention?
6.6. Summary
7. Bayesian Applications
7.1. Bayesian Networks
7.1.1. Model Structure and Conditional Probability Tables
7.1.1.1. Building a BN Model
7.1.1.2. Populating the CPTs
7.1.1.3. Discretization and Its Impacts on a BN
7.1.2. Model Diagnostics and Sensitivity Analysis for Bayesian Networks
7.1.2.1. Sensitivity to Findings
7.1.2.2. Model Validation
7.1.3. Spatio-temporal BN
7.2. Bayesian Change Point and Threshold Models
7.2.1. Hierarchical Change Point Model
7.2.2. Modeling Temporal Changes in the Flow-Concentration Relationship
8. Concluding Remarks
8.1. Model Formulation
8.2. Estimation
8.3. Model Evaluation
8.4. Statistical Significance and Bayesian Posterior Distribution
8.5. Formulating a Prior Distribution Based on Hyper-distribution
8.5.1. Example: Forecasting the Likelihood of High Cyanobacterial Toxin Concentration Events in Western Lake Erie
Bibliography
Index