Modeling Spatial Covariance Using the Limiting Distribution of Spatio-Temporal Random Walks
Journal of the American Statistical Association, 112 (518):
497-507 (2017)DOI: 10.1080/01621459.2016.1224714
Abstract
We present an approach for modeling areal spatial covariance in observed genetic allele data by considering the stationary (limiting) distribution of a spatio-temporal Markov random walk model for gene flow. This stationary distribution corresponds to an intrinsic simultaneous autoregressive (SAR) model for spatial correlation, and provides a principled approach to specifying areal spatial models when a spatio-temporal generating process can be assumed. We apply the approach to a study of spatial genetic variation of trout in a stream network in Connecticut, USA.
Description
Discusses asymmetry, with application to trout in a stream network.
Has a mixed model where the driving Gaussian noise has the covariance function
of the stationary distribution of a discrete-space-time random field.
The random field is a discrete model of abundance with sources, sinks, and migration -
reaction-diffusion with diffusion from a MC and reaction equal to births minus deaths;
and modeling the reaction term as spatial white noise.
No reasons are given why the covariance function for space-time abundance should equal
the covariance function underlying allelic identity.