Puneet Velidi

Topic

Methods for Censored Covariates, Spatial Transcriptomic Data and Neural Manifolds

Department of Mathematics and Statistics

Date & location

• Wednesday, September 9, 2026
• 11:00 A.M.
• Virtual Defence

Examining Committee

Supervisory Committee

• Dr. Dr. Farouk Nathoo, Department of Mathematics and Statistics, University of Victoria (Co-Supervisor)
• Dr. Michelle Miranda, Department of Mathematics and Statistics, UVic (Co-Supervisor)
• Dr. Enrico Amico, School of Mathematics, University of Birmingham (Outside Member)
• Dr. Tanya Garcia, Department of Biostatistics, University of North Carolina at Chapel Hill (Outside Member)
• Dr. Maryclare Griffin, Department of Mathematics and Statistics, University of Massachusetts Amherst (Outside Member)

External Examiner

• Dr. Jörn Diedrichsen, Computational Neuroscience, University of Western Ontario

Chair of Oral Examination

• Dr. George Tzanetakis, Department of Computer Science, UVic

Abstract

This thesis develops statistical methods in three areas. The first is a new semiparametric Bayesian model for survival analysis with a right-censored covariate, with application to survival and neuroimaging data in Huntington’s disease. The second is an investigation of nonstationary spatial covariance in spatial transcriptomic data. The third is an investigation of within-region of interest (ROI) principal components for brain fingerprinting.

In the first chapter, we develop SPARTACCUS (SemiPArametric Right-censored event Time and Censored Covariate as USual), a Bayesian joint model with semiparametric Cox proportional hazards models for both a right-censored response and a censored covariate. Survival models incorporating censored covariates are useful for understanding Huntington’s disease progression because subject observation often ends before the initial presentation of symptoms. Modeling both a censored response and censored covariate is challenging because ordering constraints lead to non-independent censoring mechanisms. In simulations, SPARTACCUS drastically outperforms a complete-case Cox proportional hazards analysis in high-censoring settings across a range of sample sizes and hazard shapes. We apply our method to the PREDICT-HD clinical trial, where the censored response and censored covariate are ordered Huntington’s disease stages and the uncensored covariates are cortical lobar brain volumes.

The second chapter investigates spatial correlation in spatial transcriptomic data. Gaussian process-based models underlie many popular spatial transcriptomics tools and assume stationary covariance in their kernels. We test this assumption across 13 Visium datasets using approximate Bayes factors from R-INLA to compare stationary and nonstationary Matérn covariance functions. Across tissues, between 5% and 50% of genes show evidence for covariance nonstationarity. Although methods for spatial gene-expression analysis have not generally considered covariance nonstationarity, our results suggest that spatial transcriptomic data can exhibit substantial nonstationarity. In addition to being an important feature of the data, spatial nonstationarity leads to a new categorization of spatially varying genes.

The third and final research chapter investigates brain fingerprinting and dimension reduction. Neural activity is organized on low-dimensional manifolds, yet standard functional connectivity in functional MRI usually represents each parcel by a single average of its voxel time series. We instead represent each parcel by principal-component time series spanning a low-dimensional blood-oxygen-level-dependent subspace and use the RV coefficient to measure connectivity between these subspaces. We show that within-ROI principal-component manifold connectomics exposes identity- and task-dependent structure hidden by scalar regional summaries, providing a practical framework for mapping connectivity between low-dimensional neural representations.