This article was originally published here
Biometrics. November 22, 2021. doi: 10.1111 / biom.13602. Online ahead of print.
Spatial partitioning methods correct the non-stationarity of spatially related data by partitioning the space into regions of local stationarity. Existing spatial partitioning methods can only estimate linear partitioning limits. This is insufficient to detect an anomalous spatial region of arbitrary shape in a larger area. We propose a novel Bayesian Functional Spatial Partitioning (BFSP) algorithm that estimates closed curves that act as partitioning boundaries around anomalous regions of data with a distinct spatial distribution or process. Our method uses transitions between a fixed Cartesian coordinate system and a moving polar coordinate system to model smooth boundary curves using functional estimation tools. Using adaptive Metropolis-Hastings, the BFSP algorithm simultaneously estimates the partitioning boundary and the parameters of the spatial distributions within each region. Through simulation, we show that our method is robust to the shape of the target area and to region-specific spatial processes. We illustrate our method through the detection of cancerous lesions of the prostate using magnetic resonance imaging. This article is protected by copyright. All rights reserved.