Spatial partitioning methods correct for nonstationarity in spatially related data by partitioning the space into regions of local stationarity. Existing spatial partitioning methods can only estimate linear partitioning boundaries. This is inadequate for detecting an arbitrarily shaped anomalous spatial region within a larger area. We propose a novel Bayesian functional spatial partitioning (BFSP) algorithm, which estimates closed curves that act as partitioning boundaries around anomalous regions of data with a distinct distribution or spatial process. Our method utilizes transitions between a fixed Cartesian and moving polar coordinate system to model the 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 shape of the target zone and region-specific spatial processes. We illustrate our method through the detection of prostate cancer lesions using magnetic resonance imaging.
Bibliographical noteFunding Information:
This work was supported by NCI R01 CA241159, NIBIB P41 EB027061, and the Assistant Secretary of Defense for Health affairs, through the Prostate Cancer Research Program under Award No. W81XWH‐15‐1‐0478.
© 2021 The International Biometric Society
- biomedical imaging
- functional estimation
- spatial partitioning
- spatial statistics
PubMed: MeSH publication types
- Journal Article