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Abstract Details

Activity Number: 448
Type: Topic Contributed
Date/Time: Wednesday, August 1, 2012 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistics in Epidemiology
Abstract - #306073
Title: Bayesian Inference on Constrained Parameter Spaces of Functional Mixed Models
Author(s): Sarat C Dass*+
Companies: Michigan State University
Address: Department of Statistics and Probability, East Lansing, MI, , USA
Keywords: functional data analysis ; linear mixed models ; splines ; Bayesian analysis
Abstract:

This talk develops estimation and testing methodology for multivariate functional response data modeled non-parametrically using fixed and random spline coefficients. Of particular interest is the development of methodology for pre-specified covariance matrix forms of the random coefficients, which translate to constraints on the (matrix) entries. The Bayesian testing approach proposed requires the development of default prior elicitation on the constrained positive definite spaces. The statistical methodology is developed in direct response to studying the impact of human activity on biodiversity in the Upper Peninsula of Michigan. Audio measurements taken at regular time intervals are converted to energy readings corresponding to 12 frequency bands for different categories of wildlife. These energy readings thus constitute multivariate functional data; pre-specified constraints on the covariance matrix entries determine the extent of impact of human activity on wildlife at the different frequency bands. Methodology is also developed for determining whether these constraints differ for spatial locations that vary according to their degree of pristineness.


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