CS01: Advanced Bayesian Methods and Statistical Innovations in High-Dimensional Mixed-Type Data Analysis and Neuroimaging

date: 7/15/2025, time: 14:00-15:30, room: IM WS

Organizer: Hsin-Hsiung Huang (University of Central Florida)

Chair: Hsin-Hsiung Huang (University of Central Florida)

A Statistical Reconstruction Algorithm for 3D Positronium Lifetime Imaging with Time-of-Flight PET

Hsin-Hsiung (University of Central Florida)

Positronium Lifetime Imaging (PLI) is an advanced functional imaging modality that extends conventional time-of-flight (TOF) positron emission tomography (PET) to enable probing of the tissue microenvironment. A central challenge in PLI is the accurate reconstruction of lifetime images from list-mode data, as the finite TOF resolution of scanners convolves the inherent exponential decay of positronium with the system’s Gaussian-like temporal response function. This paper introduces a robust statistical algorithm for high-fidelity PLI. Building upon our foundational work on 2D reconstruction published in IEEE TPMRS, we present a significant extension of our method to full 3D PLI image reconstruction. Our approach is based on a maximum likelihood estimation (MLE) framework that employs an exponentially modified Gaussian (EMG) probability distribution to precisely model the measured lifetime data. Through comprehensive computer simulations, we demonstrate that the proposed EMG-based MLE method yields quantitatively accurate 3D lifetime images and outperforms conventional approaches based on simpler exponential likelihoods. The framework also effectively handles data containing multiple positron populations, providing a robust and accurate tool to realize the full potential of 3D PLI in pre-clinical and clinical research.

Bayesian Sparse Kronecker product decomposition

Shao Hsuan Wang (National Central University, Taiwan)

Bayesian Sparse Kronecker product decomposition

The Sparse Kronecker Product Decomposition (SKPD) for tensor data was introduced by Sanyou Wu and Long Feng (2023). This method represents the first frequentist framework designed for signal region detection in high-resolution, high-order image regression problems. Their work demonstrated the strong performance of SKPD in various applications.
In this presentation, we will introduce a Bayesian version of SKPD, referred to as Bayesian SKPD. From a Bayesian perspective, we apply a three-parameter beta-normal prior family to the parameters of interest. Additionally, we address tensor regression data with mixed-type responses using Polya-Gamma augmentation. This approach allows us to give credible region detection through direct Gibbs sampling. The theoretical results will be presented, and we will demonstrate the effectiveness of Bayesian SKPD using real brain imaging data from the OASIS.

Low-rank regularization of Fréchet regression models for distribution function response

Kyunghee Han (University of Illinois Chicago)

Fréchet regression has emerged as a useful tool for modeling non-Euclidean response variables associated with Euclidean covariates. In this work, we propose a global Fréchet regression estimation method that incorporates low-rank regularization. Focusing on distribution function responses, we demonstrate that leveraging the low-rank structure of the model parameters enhances both the efficiency and accuracy of model fitting. Through theoretical analysis of the large-sample properties, we show that the proposed method enables more robust modeling and estimation than standard dimension reduction techniques. We also present numerical experiments that evaluate the finite-sample performance to support our findings.