| Fish are like trees, except they are
invisible and they move: John Shepherd |
Most
fisheries
and other wildlife professionals
who are tasked with providing scientific advice to decision makers
often find
existing software tools insufficient for their needs, requiring the
development of purpose-built computer programs. The primary bases for
quantitative scientific advice are the results of statistical analyses
and
model-fitting exercises. The objective of this course is to
expose students who have taken courses in mathematical modeling and
statistical model fitting to numerical methods. Modeling
environments such as EXCELTM and Visual BasicTM
are sufficient for conducting several types of analyses, but more
powerful techniques are often needed to solve research questions. The
focus of this course will be on fisheries applications, but the models
and techniques to be covered are broadly applicable in
quantitative conservation biology.
The course is based on four major themes:
- how to use R to perform numerical analyses;
- how to use AD Model Builder (ADMB)TM to fit
models to data;
- how to use WINBUGS
to implement Bayesian hierarchical models; and
- standard numerical techniques.
The ADMB component of the course will introduce students to
how
to write ADMB programs to minimize multiparameter non-linear
functions, in particular, likelihood functions. It will also outline
how to use ADMB to compute likelihood profiles and Bayesian posterior
distributions for model parameters and model outputs. The examples will
be based on fitting exponential growth and size-structured models.
The numerical methods section of the course will introduce students
to numerical differentiation and integration, interpolation and how to
generate random numbers.
The R component of the course will focus on how to use R to
implement the numerical methods covered during the course, as well as
how to use R when fitting models using ADMB.
The WINBUGS component of the course will introduce students
to the use of the WINBUGS package for implementing Bayesian hierarchical models. The use of WINBUGS
will focus on how to conduct a meta-analysis.
Numerical techniques should not be applied "cookbook"
style. It
is necessary to understand the mathematical basis for the technique.
Furthermore, numerical techniques frequently involve expert judgment
regarding choices (e.g. for tolerances, initial values). The best way
to learn a numerical technique therefore involves knowing its
theoretical basis and spending
time practicing it. This course will attempt to cover both aspects.
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