Collaborative Research: Novel Bayesian Thresholding and Shrinkage Methods in Multiscale Domains with Applications

Modern science and engineering increasingly rely on extracting meaningful information from large and noisy datasets, such as those arising in medical imaging, environmental monitoring, telecommunications, and numerous other disciplines. This project develops advanced statistical methods that improve signal recovery and noise reduction through innovative shrinkage and thresholding techniques applied in multiscale domains like wavelets. In addition to classical computational tools, the project explores emerging directions involving quantum computing simulators to prototype quantum-inspired shrinkage methods, aligning with growing national and institutional emphasis on quantum technologies. These approaches simplify complex data by selectively attenuating noise while preserving essential features, leading to more accurate and interpretable results. The project integrates education by mentoring students at multiple levels, incorporating findings into graduate and undergraduate courses, and creating open-source software tools that promote reproducible research and broad access to cutting-edge statistical techniques. This research advances the theory and application of shrinkage estimation in multiscale settings, with a particular emphasis on quantum-inspired methodologies that complement classical Bayesian and frequentist frameworks. It develops adaptive block-shrinkage procedures employing priors that capture dependence among wavelet coefficients and introduces absolutely continuous shrinkage priors that maintain computational tractability without relying on spike-and-slab or point-mass priors. The project also devises novel thresholding strategies informed by refined extreme-value approximations and Bayesian decision rules based on Bayes factors. Computational implementation includes efficient posterior simulation algorithms and exploratory shrinkage techniques using quantum computing simulators. These innovations will contribute to foundational methodology for nonparametric regression, signal processing, and scalable high-dimensional inference. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.