STATS 331: Introductory Bayesian Data Analysis:
Second Semester 2010
Taught by Dr. Wayne S. Stewart
The title
is "Introductory
Bayesian Data Analysis".
The
paper starts with a
brief history of Statistics, and demonstrates that the Bayesian
paradigm
was basically how Statistics was originally done and how it went out of
favour,
to be largely replaced by the frequentist paradigm (which we call
classical and
is what you have been taught up till now) only to flourish again
in the
last 30 or so years due to the advancement of the computer and the
mathematics
of MCMC (Monte Carlo Markov Chains), the
combination of which has meant that Bayesian statistics is doable and
is
capable of answering questions that the classical methods cannot.
The course
will give an
introduction to some of the principles that are foundational to the
Bayesian
paradigm (like the Likelihood principle), along with a number of
philosophical
issues like the conditionality priniciple and Stopping rule
principle.
The
Bayesian approach will be
introduced through discrete distributions using "Bayes Box". The
parameter is treated as a Random Variable with a probability density
function. The
prior reflects prior knowledge, which is updated with the
likelihood to form the latest understanding of the parameter
called the
posterior.
The course
will show methods of
summarizing the posterior, including Highest density intervals and
Bayesian
credible regions and give details on how to practically carry out
a fully Bayesian
analysis.
Basics of
Bayesian simulation will
be taught with rejection sampling and MCMC as a black box. Only the
absolute
mathematical necessities will be taught with most emphasis given to the
practical
implementation and interpretation.
WinBUGS will be
the main software used to do the simulations and
construct and run the models. Time will be given to learn and
understand how to
use this software. Indeed the two software packages used in the course
will be
R and WinBUGS. Interestingly,
WinBUGS
can be run from within R and this will be covered also.
Model
checking will be taught using Bayes
factors, predictive
distributions and DIC.
A major
part of the course will be
to re-run analyses and methods you are already familiar with and
compare
results and interpretations with the Bayesian conclusions.
ANOVA,
regression, one, two sample
t-tests, Hierarchical methods and time series will be given a Bayesian
treatment.
This
course will be an EYE -opener -- you
will be shocked at some of the comparisons we make
with classical methods.
We will
look at the probability of
the posterior NULL hypothesis and compare this with the classical
P-Value for a
number of problems.
Many new
insights into statistics
will be demonstrated.
For more
information contact
Office
303.294
Ph. 373
7599 X83763