Hani Doss
Department of Statistics
Ohio State University
TITLE:
A computing environment for visualization of posterior distributions
obtained from MCMC output.
ABSTRACT:
In a Bayesian analysis one fixes a prior on the unknown parameter,
observes the data, and obtains the posterior distribution of the
parameter given the data. But what about the choice of the prior?
Ideally, one would want to know posterior distributions for a wide
variety of priors. If the posterior does not change much when
one
changes the prior then one gets a feeling of reassurance---a
different investigator with a slightly different prior may not even
bother to recompute the posterior for his prior. On the other
hand,
if the posterior changes significantly when one changes the prior,
then it is important to record that fact, so that for example more
time is spent on prior elicitation. Therefore, in almost any
problem in which one carries out a serious data analysis, one wants
to calculate the posterior distribution for a large number of prior
distributions, especially in the exploratory stages of the analysis.
In many problems, the posterior is estimated through Markov chain
Monte Carlo, which may require non-negligible computer time, and
unfortunately this precludes consideration of a large number of
priors and an interactive analysis. To deal with this problem,
I
will present a computing environment, currently still under
development, within which one can interactively change the prior and
immediately see the corresponding changes in the posterior. The
environment is based on an importance sampling procedure which
enables one to use the output of one or a small number of Markov
chains to obtain estimates of the posterior for a large class of
priors, and runs on Splus/R (the current implementation runs in
LISP-STAT). The environment is very general and handles a wide
range of standard models, including for example GLM's and
hierarchical models. This is joint work with B. Narasimhan of
Stanford University.
Seminar to be held in Room 107, 24 Hillhouse at 4:15 pm