Making statistical modeling and inference more accessible to ecologists and related scientists, Introduction to Hierarchical Bayesian Modeling for Ecological Data gives readers a flexible and effective framework to learn about complex ecological processes from various sources of data. It also helps readers get started on building their own statistical models.
The text begins with simple models that progressively become more complex and realistic through explanatory covariates and intermediate hidden states variables. When fitting the models to data, the authors gradually present the concepts and techniques of the Bayesian paradigm from a practical point of view using real case studies. They emphasize how hierarchical Bayesian modeling supports multidimensional models involving complex interactions between parameters and latent variables. Data sets, exercises, and R and WinBUGS codes are available on the authors’ website.
This book shows how Bayesian statistical modeling provides an intuitive way to organize data, test ideas, investigate competing hypotheses, and assess degrees of confidence of predictions. It also illustrates how conditional reasoning can dismantle a complex reality into more understandable pieces. As conditional reasoning is intimately linked with Bayesian thinking, considering hierarchical models within the Bayesian setting offers a unified and coherent framework for modeling, estimation, and prediction.
Table of Contents
I Basic Blocks of Bayesian Modeling
Bayesian Hierarchical Models in Statistical Ecology
Challenges for statistical ecology
Conditional reasoning, graphs and hierarchical models
Bayesian inferences on hierarchical models
What can be found in this book?
The Beta-Binomial Model
From a scientific question to a Bayesian analysis
What is modeling?
Think conditionally and make a graphical representation
Inference is the reverse way of thinking
Encoding prior knowledge
The conjugate Beta pdf
Bayesian inference as statistical learning
Bayesian inference as a statistical tool for prediction
Asymptotic behavior of the beta-binomial model
The beta-binomial model with WinBUGS
The Basic Normal Model
Salmon farm’s pollutants and juvenile growth
A Normal model for the fish length
Normal-gamma as conjugate models to encode expertise
Inference by recourse to conjugate property
Working with More Than One Beta-Binomial Element
Successive removal analysis
Testing a new tag for tuna
Combining Various Sources of Information
Stochastic model for salmon behavior
Inference with WinBUGS
Discussion and conclusions
The Normal Linear Model
The decrease of Thiof abundance in Senegal
Linear model theory
A linear model for Thiof abundance
Nonlinear Models for Stock-Recruitment Analysis
Stock-recruitment motivating example
Searching for a SR model
Changing the error term from lognormal to gamma
From Ricker to Beverton and Holt
Model choice with informative prior
Conclusions and perspectives
Getting beyond Regression Models
Logistic and probit regressions
Ordered probit model
II More Elaborate Hierarchical Structures
HBM I: Borrowing Strength from Similar Units
HBM for capture-mark-recapture data
Hierarchical stock-recruitment analysis
Further Bayesian comments on exchangeability
HBM II: Piling up Simple Layers
HBM for successive removal data with habitat and year
Electrofishing with successive removals
HBM III: State-Space Modeling
State-space modeling of a biomass production model
State-space modeling of Atlantic salmon life cycle model
A tool of choice for the ecological detective
Decision and Planning
The Sée-Sélune river network
Salmon life cycle dynamics
Long-term behavior: Collapse or equilibrium?
Management reference points
Management rules and implementation error
Appendix A: The Normal and Linear Normal Model
Appendix B: Computing Marginal Likelihoods
Appendix C: The Baseball Players’ Historical Example
Appendix D: More on Ricker Stock-Recruitment
Éric Parent is head of the Research Laboratory for Risk Management in Environmental Sciences (Team MORSE) and a professor in applied statistics and probabilistic modeling for environmental engineering at the National Institute for Rural Engineering, Water and Forest Management (ENGREF/AgroParisTech) in Paris, France. Dr. Parent’s research encompasses Bayesian theory and applications, with special emphasis on environmental systems modeling.
Étienne Rivot is a researcher in the Fisheries Ecology Laboratory at Agrocampus Ouest in Rennes, France. Dr. Rivot’s research focuses on the application of Bayesian statistical modeling for the analysis of ecological data, inference, and predictions.
"This book is a welcome addition to the Bayesian literature. It is well written and amply illustrates Bayesian methods with practical applications in fisheries management. The programs for data analyses are available on the book’s website, allowing users to get their ‘hands dirty’ and in the process really understand the model construction and the software."
— Subhash R. Lele, Ecology, 95(1), 2014
"The book is well written and easy to read, and the material presented deserves a greater exposure in taught statistics courses. I thoroughly recommend the book and believe that the statistical techniques and their application to quantitative fisheries science could ideally complement a short undergraduate course in applied statistics."
—Carl M. O’Brien, International Statistical Review (2013), 81