Sponsoring Section/Society: ASA-SBSS
Session Slot: 10:30-12:20 Thursday
Estimated Audience Size: 100
AudioVisual Request: Overhead Projector, Slide Projector
Session Title: Bayesian Generalized Linear Models
The role of the statistician in public policy is to help
stakeholders effectively use information and accurately quantify
uncertainty when making decisions. This often requires blending of
information from many samples or sites. This blending creates several
problems: 1) the increased heterogeniety observed across samples is
not accounted for using conventional models, 2) geographic correlation
of samples may need to be incorporated, and 3) estimates may be needed
at both local and global levels. Bayesian hierarchical models
are especially well suited to solving these problem. In this session
speakers will discuss how Bayesian Generalized Linear Models can be
used to solve these problems using examples from environmental
monitoring, geographic and temporal disease mapping, and risk
assessment.
Theme Session: No
Applied Session: No
Session Organizer: Sun, Dongchu University of Missouri
Address: Dongchu Sun Department of Statistics University of Missouri Columbia, MO 65211
Phone: 573-882-7675
Fax: 573-884-5524
Email: dsun@stat.missouri.edu
Session Timing: 110 minutes total (Sorry about format):
Opening Remarks by Chair - 5 First Speaker - 30 minutes Second Speaker - 30 minutes Third Speaker - 30 minutes Discussant - 10 minutes Floor Discusion - 5 minutes
Session Chair: Speckman, Paul L. University of Missouri-Columbia
Address: Paul L. Speckman Department of Statistics 222 Math Sciences Building University of Missouri-Columbia Columbia, MO 65211
Phone: 860-486-3414
Fax: 860-486-4113
Email: dey@stat.uconn.edu
1. Overdispersed Generalized Linear Models
Dey, Dipak K., University of Connecticut
Address: Dipak K. Day Department of Statistics University of Connecticut Storrs, CT 06269-3120
Phone: 860-486-3414
Fax: 860-486-4113
Email: dey@stat.uconn.edu
Abstract: Generalized linear models have become a standard class of models for data analysts. However in some applications, heterogeneity in samples is too great to be explained by the simple variance function implicit in such models. A two parameter exponential family which is overdispersed relative to a specified one parameter exponential family yields a the class of overdispersed generalized linear models (OGLM's) which are analytically attractive. We propose fitting such models within a Bayesian framework employing noninformative priors in order to let the data drive the inference. Hence our analysis approximates likelihood-based inference but provides an entire posterior distribution for model parameters. Bayesian calculations are carried out using a Metropolis sampling algorithm. An example involving damage incidents to cargo ships motivates our work. Details of the data analysis are provided including comparison with the standard generalized linear models analysis. Several diagnostic tools reveal the improved performance of the OGLM.
2. Hierarchical and Empirical Bayes Methods for Environmental Risk Assessment
Sankar, Gauri Sankar, University of Georgia
Address: Gauri Sankar Datta Department of Statistics University of Georgia Athens, GA 30602
Phone: 301-457-4728
Fax: 301-457-2299
Email: gauri@stat.uga.edu
Ghosh, Malay, University of Florida
Waller, Lance A., University of Minnesota
Abstract: The cancer and other disease atlases have become important tools for environmental monitoring and risk assessment. To study geographical variation in incidence of disease and mortality rates for local areas preparation of these maps has received considerable attention in recent years. Such maps usually display either relative rates in each area, as measured by a standardized mortality ratio (SMR), or p-values based on some statistical tests. None of these methods is entirely satisfactory. The raw SMR estimates are often based on small sample sizes, and hence are usually unreliable. In order to borrow strength from the local areas and to smooth the raw estimates a model-based procedure is often appropriate. We will review the recent developments in hierarchical Bayes generalized linear models including random effects for local areas. Both hierarchical and empirical Bayes estimation will be considered.
3. Default Bayesian Analysis for Generalized Linear Model
Sun, Dongchu, University of Missouri
Address: Dongchu Sun Department of Statistics University of Missouri Columbia, MO 65211
Phone: 573-882-7675
Fax: 573-884-5524
Email: dsun@stat.missouri.edu
Tsutakawa, Robert, University of Missouri
Abstract: Bayesian analysis for a generalized linear model, where the prior follows a hierarchical linear mixed model, has received much attention recently. In practice, it is often very difficult to choose the hyperparameters. This paper first gives necessary and sufficient conditions for the propriety of the posterior distribution in hierarchical linear mixed effects models for a collection of improper prior distributions. In addition to the flat prior for the fixed effects, the collection includes various limiting forms of the invariant gamma distribution for the variance components, including cases considered previously by Datta and Ghosh (1991), Datta (1992), and Hobert and Casella (1996). Previous work is extended by considering a family of correlated random effects which include as special cases the CAR (1) models by Besag, York and Mollie (1991) and Clayton and Kaldor (1987) and autoregressive model by Ord (1975), which have been found useful in the analysis of spatial effects. A noninformative prior for the spatial correlation coefficients are also examined. Conditions are then presented for the propriety of the posterior distribution for generalized linear mixed models. The methods are successfully applied for estimating the mortality or disease rates including demographic variables such as age and sex, random geographic variables such as regional differences, longitudinal variables such as temporal trends in mortality, and spatial variables such as the correlation between neighboring regions.
Discussant: Albert, Jim Bowling Green State University
Address: Jim Albert Department of Mathematics and Statistics Bowling Green State University Bowling Green, OH 43403
Phone: 419-372-7456
Fax: 419-372-6092
Email: albert@math.bgsu.edu
List of speakers who are nonmembers: None