A novel Bayesian functional spatial partitioning method with application to prostate cancer lesion detection using...

Area of Science:

• Spatial statistics
• Geostatistics
• Computational statistics

Background:

• Spatial partitioning methods address nonstationarity in spatial data by dividing space into stationary regions.
• Current methods are limited to linear boundaries, failing to detect arbitrarily shaped anomalous regions.
• Accurate detection of complex spatial anomalies is crucial in various scientific fields.

Purpose of the Study:

• To develop a novel Bayesian functional spatial partitioning (BFSP) algorithm.
• To enable the estimation of non-linear, closed curve boundaries around anomalous spatial regions.
• To improve the detection of arbitrarily shaped anomalous regions with distinct spatial processes.

Main Methods:

• The Bayesian functional spatial partitioning (BFSP) algorithm utilizes transitions between Cartesian and polar coordinate systems.
• Functional estimation tools are employed to model smooth, closed boundary curves.
• Adaptive Metropolis-Hastings sampling is used for simultaneous estimation of boundaries and spatial distribution parameters.
• Simulations assess the method's robustness to target zone shape and region-specific spatial processes.

Main Results:

• The BFSP algorithm successfully estimates non-linear partitioning boundaries around anomalous regions.
• The method demonstrates robustness to various target zone shapes and underlying spatial processes.
• Simulations confirm the algorithm's effectiveness in identifying distinct spatial distributions.

Conclusions:

• The proposed BFSP algorithm offers a significant advancement over existing spatial partitioning methods.
• This novel approach accurately detects arbitrarily shaped anomalous regions and their associated spatial processes.
• The method has practical applications, such as in medical imaging for detecting prostate cancer lesions.