Random Fields and Statistical Models for Circuits

• Activity Number: 251
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Ephraim Hanks*+ and Mevin Hooten
• Companies: California State University and Colorado State University
• Keywords: Markov random fields ; Landscape genetics ; Circuit theory ; Conditional autoregressive models

Abstract

Circuit theory has seen extensive recent use in the field of ecology, where it is often applied to study nonstationary functional connectivity. In these cases, the landscape is typically represented by a network of nodes and resistors, with the resistance between nodes a function of landscape characteristics. The effective distance between two locations on a landscape is represented by the resistance distance, as defined by circuit theory, between the nodes in the network. Circuit theory has been applied to many other scientific fields for exploratory analyses, but parametric models for circuits are not common in the scientific literature. To model circuits explicitly, we demonstrate a link between Gaussian Markov random fields and contemporary circuit theory using a covariance structure that induces the necessary resistance distance. This provides a parametric model for observations from system represented by circuits. In the landscape ecology setting, this model provides a simple framework where inference can be obtained for effects that landscape features have on functional connectivity.