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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 commentedR 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 generalizedto 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 binomialGLMs. 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 themean
” (Chapter 4), is made progressively more complex until we havea 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.
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