Spatiotemporal signal detection using continuous shrinkage priors.

Periodontal disease (PD) is a chronic inflammatory disease that affects the gum tissue and bone supporting the teeth. Although tooth-site level PD progression is believed to be spatio-temporally referenced, the whole-mouth average periodontal pocket depth (PPD) has been commonly used as an indicator of the current/active status of PD. This leads to imminent loss of information, and imprecise parameter estimates. Despite availability of statistical methods that accommodates spatiotemporal information for responses collected at the tooth-site level, the enormity of longitudinal databases derived from oral health practice-based settings render them unscalable for application. To mitigate this, we introduce a Bayesian spatiotemporal model to detect problematic/diseased tooth-sites dynamically inside the mouth for any subject obtained from large databases. This is achieved via a spatial continuous sparsity-inducing shrinkage prior on spatially varying linear-trend regression coefficients. A low-rank representation captures the nonstationary covariance structure of the PPD outcomes, and facilitates the relevant Markov chain Monte Carlo computing steps applicable to thousands of study subjects. Application of our method to both simulated data and to a rich database of electronic dental records from the HealthPartners ® Institute reveal improved prediction performances, compared with alternative models with usual Gaussian priors for regression parameters and conditionally autoregressive specification of the covariance structure.

Spatial Signal Detection Using Continuous Shrinkage Priors.

Motivated by the problem of detecting changes in two-dimensional X-ray diffraction data, we propose a Bayesian spatial model for sparse signal detection in image data. Our model places considerable mass near zero and has heavy tails to reflect the prior belief that the image signal is zero for most pixels and large for an important subset. We show that the spatial prior places mass on nearby locations simultaneously being zero, and also allows for nearby locations to simultaneously be large signals. The form of the prior also facilitates efficient computing for large images. We conduct a simulation study to evaluate the properties of the proposed prior and show that it outperforms other spatial models. We apply our method in the analysis of X-ray diffraction data from a two-dimensional area detector to detect changes in the pattern when the material is exposed to an electric field.