On Bayesian Assessment of Curvilinear Boundaries

• Activity Number: 272
• Type: Contributed
• Date/Time: Tuesday, August 10, 2004 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Sudipto Banerjee*+
• Companies: University of Minnesota
• Keywords: spatial models ; spatial gradients ; boundary assessments ; Bayesian inference ; Markov chain Monte Carlo ; Gaussian process

Abstract

Boundary analysis concerns the detection and analysis of zones of abrupt change in spatial maps. Its importance in understanding scientific phenomena has been widely recognized in genetics and ecology dating back to Womble. Although contour-mapping visually diplays lines separating such zones, these current methods are based upon rather ad hoc deterministic algorithms. This talk focuses upon a framework to carry out formal statistical inference for statistically assessing whether curvilinear boundaries (or segments thereof) delineate regions with differing responses. Line integrals of gradient processes, arising out of parent Gaussian processes, are employed to compute average gradients along boundaries. Using posterior samples from typical Markov chain Monte Carlo output from fitted spatial models, posterior distributions of analytically intractable Gaussian line integrals are computed enabling formal statistical inference. Examples of the methodology will be presented through simulated as well as real data.