Computationally efficient approximations to conditional autoregressive prior for spatial and spatiotemporal datasets over large lattices
| Authors: | Md Kamrul Hasan Khan, Avishek Chakraborty, Giovanni Petris, Ghadeer J.M. Mahdi, Barry T. (Ty) Wilson |
| Year: | 2026 |
| Type: | Scientific Journal |
| Station: | Northern Research Station |
| DOI: | https://doi.org/10.1016/j.spasta.2026.100988 |
| Source: | Spatial Statistics |
Abstract
Models for adjacency-based association represent an important branch of spatial statistics relevant for measurements associated to areal units or geographical networks. Within this domain, conditional autoregressive (CAR) prior represents a well-known tool for modeling dependence through random effects. However, the usual Markov chain Monte Carlo scheme for this framework requires sequential update of these effects from posterior full-conditional distributions resulting in poor convergence and mixing properties. In this article, we propose two alternative methods utilizing spectral properties of the Laplacian of the adjacency matrix. Our first proposal introduces a reduced-rank approximation to the CAR prior and the second proposal improves the quality of approximation by correcting for underestimation of variance parameter. These methods can be extended to any spatiotemporal setting as we have illustrated using a dynamic sequence of spatial random effects. All computational steps necessary to efficiently implement these methods, including determination of the eigen-structure of high-dimensional Laplacian matrices and derivation of posterior distributions, have been thoroughly described. Multiple simulation studies and two real-world datasets, representing diverse kinds of spatial and spatiotemporal response functions as well as adjacency structures on large number of units, are included to illustrate the utility of propose methods. Our findings adequately establish their benefits with respect to predictive performance and computational attributes.