Masotti, Maria2022-08-292022-08-292022-05https://hdl.handle.net/11299/241432University of Minnesota Ph.D. dissertation. May 2022. Major: Biostatistics. Advisors: Lin Zhang, Joseph Koopmeiners. 1 computer file (PDF); viii, 97 pages.Manual protocols to predict the number, size, and location of cancerous lesions in the prostate using imaging data are highly dependent on reader experience and expertise. Existing computer-aided voxel-wise classifiers do not directly provide estimates of lesion boundaries, which are clinically important. Spatial partitioning methods estimate boundaries separating regions of local stationarity in spatially registered data, but existing methods are inadequate for the application of lesion detection because the boundaries are restricted to be linear or piecewise linear. We first introduce a novel Bayesian functional spatial partitioning method (BFSP-1) which estimates the partitioning boundary around an anomalous region of data with a distinct distribution or spatial process. Our algorithm transitions between a fixed Cartesian and a moving polar coordinate system to model the boundary with functional estimation tools. Using adaptive Metropolis-Hastings, the BFSP-1 algorithm simultaneously estimates the partitioning boundaries and the parameters of the spatial distributions within each region. BFSP-1 assumes the data contain one and only one anomalous region. To create a more clinically useful tool, we build upon our original boundary estimation framework and propose BFSP-M for multiple region discovery. This method uses reversible jump Markov chain Monte Carlo to jointly estimate the number of lesions, their boundaries, and their distinct spatial processes. Finally, we discuss BFSP-3D, which extends the BFSP framework to three dimensions. Through simulation, we show that our methods are robust to the shape of the target zone and region-specific spatial processes. Our methods prove to be a clinically useful tool for automatic boundary drawing of cancerous lesions using non-invasive prostate imaging data.enThesis or Dissertation