Annual Report 2008.pdf - SAMSI

used to conditionally model high category events conditional upon the occurrence of a hurricane.
A Markov transition structure is used to propagate information over time.
The second paper, on the impact of various treatments on the future drinking behavior of
alcoholics, also uses a GPD structure. The goal is to determine which of three approaches- (1)
twelve step program, (2) motivational treatment, (3) behavioral therapy- does the best job of
deterring poor future drinking behavior. The novelty of the approach used here lies in the mode
of prior elicitation. It is performed on parameters in the predictive space. This differs from the
traditional approach in that we can avoid using non-informative priors on poorly understood
parameters associated with the design matrix, focusing instead on quantities that are actually
observed and thus better understood.
Sourish presented his work at a postdoc/grad student seminar while at SAMSI, and he
intends to present the second paper mentioned above at the New England Statistical Symposium
in April. He also participated in a one-day program aimed at facilitating a better understanding of
research in the mathematical sciences among undergraduate students. Each of these research
topics will also contribute a chapter to Sourish’s Ph.D. thesis.
Summary of Papers:
(a) Analyzing Extreme Hurricane Activity using Multinomial-Dirichlet Model
(b) Analyzing Fatal Drinking Behavior of Patients suffering Alcohol Dependence Disorder using
Pareto Regression
The second work above is currently being sponsored by the University of Connecticut Health
Center.
From Sourish Das
Relationship of SAMSI Research to Ph.D. Dissertation
I am developing Bayesian Method of analyzing extreme category in Multinomial-
Dirichlet model, especially, in the context of the Hurricane data of Indian Ocean (southern
hemisphere region) and Pacific Ocean (West pacific region). Here the storms are categorized into
5 categories; where estimating the probability of rare category (that is category 5 hurricane) is
challenging. This work will be a part of the 3 rd chapter of my Ph.D. dissertation.
I also developed the Bayesian analysis of Pareto Regression model with unknown shape
parameter, for excess over threshold values, designed for longitudinal studies. We developed
Pareto regression model in Generalized Linear Model (GLM) framework, using log-link between
the shape parameter of random component and systematic component of the model. We put into
practice one-step Markov transition model to embrace the longitudinal component in the model.
Then we implemented our methodology to examine the association of GABRA2 gene with fatal
alcohol intake, with the effect of psychological treatment as comparative study of efficacy of
three treatments on fatal alcohol intake.
Research Contributions
1. SAMSI Technical Report # 2007-08 “On Bayesian Analysis of Generalized Linear
Models: A New Perspective”
2. SAMSI Technical Report # 2007-09 “On Bayesian Inference for Generalized
Multivariate Gamma Distribution”