SOCR News AmStats SIM 2024

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SOCR News & Events: 2024 2024 American Statistical Association Special Session on Longitudinal Imaging and Biostatistical Methods, Statistics in Imaging Annual Meeting, Indianapolis

Spacekime Analytics Tutorial

Tutorial Logistics

Abstract

This tutorial will describe the novel complex-time (kime) representation of repeated measurement longitudinal processes, which underlies advanced space-kime statistical inference and space-kime artificial intelligence (AI) applications. By translating fundamental quantum mechanics principles into statistical inference models of time-varying processes, we generalize the classical 4D spatiotemporal sampling to a 5D space-kime manifold, where the phase of complex-time encodes repeated random drawings at fixed spatiotemporal locations. Many AI applications and statistical inference techniques involving temporal data can be formulated in a Bayesian space-kime analytics framework. We explore alternative strategies for translating time-series observations into kime-surfaces, which are richer, computationally tractable, objects amenable to tensor-based linear modeling and model-free inference. Simulated and observed neuroimaging and macroeconomics data will be used to demonstrate applications of space-kime analytics. As time permits, we may discuss the space-kime analytic duality between theoretical model inference, based on generalized functions (distributions), and experimental data inference, based on replicated finite samples as proxy measures of the underlying probability distributions. Several theoretical, experimental, computational, and data-analytic open problems will be presented.


Special Session

This session will include a blend of mathematical, statistical, and computational experts presenting on recent methodological advances to represent, model, predict, synthesize, and analyze large and heterogeneous spatiotemporal imaging data.


Session Logistics

Session Presenters

Title: Supervised Modeling of Heterogeneous Networks: Investigating Functional Connectivity Across Various Cognitive Control Tasks
Abstract: We present a neuroimaging-driven study examining the relationship between functional connectivity across cognitive control domains and cognitive phenotypes, aiming to identify specific brain regions significantly associated with these phenotypes. We propose a generalized linear modeling framework incorporating multiple network responses and predictors, allowing for diverse interconnections between edges. Leveraging hierarchical Bayesian modeling, our approach estimates regression coefficients and identifies predictor-linked nodes with precise uncertainty quantification. Theoretical analysis shows our model's posterior predictive density asymptotically approaches the true data generating density. Empirical investigations, including simulation studies and functional connectivity data analysis, demonstrate our framework's superior performance compared to competitors.


Title: Tensor Regression for Brain Imaging Data
Title: Tensor-on-Tensor Time Series Regression for Integrated fMRI Analysis (current work)
Title: (TBD)
Title: Spacekime analytics: from time-series to kime-surfaces and inference-functions


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