This book is a gentle introduction to applied Bayesian modeling for

ecologists using the highly acclaimed, free WinBUGS software, as run

from program R. The bulk of the book is formed by a very detailed yet,

I hope, enjoyable tutorial consisting of commented example analyses.

These form a progression from the trivially simple to the moderately complex

and cover linear, generalized linear (GLM), mixed, and generalized

linear mixed models (GLMMs). Along the way, a comprehensive and largely

nonmathematical overview is given of these important model classes,

which represent the core of modern applied statistics and are those which

ecologists use most in their work. I provide complete R and WinBUGS

code for all analyses; this allows you to follow them step-by-step and in

the desired pace. Being an ecologist myself and having collaborated with

many ecologist colleagues, I am convinced that the large majority of us

best understands more complex statistical methods by first executing

worked examples step-by-step and then by modifying these template

analyses to fit their own data.

All analyses with WinBUGS are directly compared with analyses of the

same data using standard R functions such as lm(), glm(), and lmer().

Hence, I would hope that this book will appeal to most ecologists regardless

of whether they ultimately choose a Bayesian or a classical mode of

inference for their analyses. In addition, the comparison of classical and

Bayesian analyses should help demystify the Bayesian approach to statistical

modeling. A key feature of this book is that all data sets are simulated

(=“assembled”) before analysis (=“disassembly”) and that fully commented

R code is provided for both. Data simulation, along with the powerful,

yet intuitive model specification language in WinBUGS, represents a

unique way to truly understand that core of applied statistics in much

of ecology and other quantitative sciences, generalized linear models

(GLMs) and mixed models.

This book traces my own journey as a quantitative ecologist toward an

understanding of WinBUGS for Bayesian statistical modeling and of

GLMs and mixed models. Both the simulation of data sets and model fitting

in WinBUGS have been crucial for my own advancement in these

respects. The book grew out of the documentation for a 1-week course

that I teach at the graduate school for life sciences at the University of

Zürich, Switzerland, and elsewhere to similar audiences. Therefore, the

typical readership would be expected to be advanced undergraduate,

xv

graduate students, and researchers in ecology and other quantitative

sciences. To maximize your benefits, you should have some basic knowledge

in R computing and statistics at the level of the linear model (LM)

(i.e., analysis of variance and regression).

After three introductory chapters, normal LMs are dealt with in

Chapters 4–11. In Chapter 9 and especially Chapter 12, they are generalized

to contain more than a single stochastic process, i.e., to the (normal)

linear mixed model (LMM). Chapter 13 introduces the GLM, i.e., the

extension of the normal LM to allow error distributions other than the

normal. Chapters 13–15 feature Poisson GLMs and Chapters 17–18 binomial

GLMs. Finally, the GLM, too, is generalized to contain additional

sources of random variation to become a GLMM in Chapter 16 for a Poisson

example and in Chapter 19 for a binomial example. I strongly believe

that this step-up approach, where the simplest of all LMs, that “of the

mean” (Chapter 4), is made progressively more complex until we have

a GLMM, helps you to get a synthetic understanding of these model

classes, which have such a huge importance for applied statistics in ecology

and elsewhere.

The final two main chapters go one step further and showcase two

fairly novel and nonstandard versions of a GLMM. The first is the siteoccupancy

model for species distributions (Chapter 20; MacKenzie et al.,

2002, 2003, 2006), and the second is the binomial (or N-) mixture model for

estimation and modeling of abundance (Chapter 21; Royle, 2004). These

models allow one to make inference about two pivotal quantities in

ecology: distribution and abundance of a species (Krebs, 2001). Importantly,

these models fully account for the imperfect detection of occupied

sites and individuals, respectively. Arguably, imperfect detection is a hallmark

of all ecological field studies. Hence, these models are extremely useful

for ecologists but owing to their relative novelty are not yet widely

known. Also, they are not usually described within the GLM framework,

but I believe that recognizing how they fit into the larger picture of linear

models is illuminating. The Bayesian analysis of these two models offers

clear benefits over that by maximum likelihood, for instance, in the ease

with which finite-sample inference is obtained (Royle and Kéry, 2007), but

also just heuristically, since these models are easier to understand when fit

in WinBUGS.

Owing to its gentle tutorial style, this book should be excellent to teach

yourself. I hope that you can learn much about Bayesian analysis using

WinBUGS and about linear statistical models and their generalizations

by simply reading it. However, the most effective way to do this obviously

is by sitting at a computer and working through all examples, as well as

by solving the exercises. Fairly often, I just give the code required to produce

a certain output but do not show the actual result, so to fully grasp

what is happening, it is best to execute all code.