About

I am a PhD candidate in Statistics at Simon Fraser University. My research focuses on statistical methodology for longitudinal and high-dimensional data, particularly when observations are sparse, irregular, and structurally complex.

I am especially interested in functional data analysis, neuroimaging, survival analysis, and statistical machine learning. I aim to develop methods that are both theoretically principled and useful for scientific applications.

Projects

Three rounds of beam search: update, select, and explore smoothing parameters during online learning.

Functional data · Online learning

OnlineFPCA

Online functional principal component analysis for streaming multidimensional data. We combine spline representations with Riemannian stochastic gradient descent to learn smooth, orthonormal components, and use beam search with rolling validation to tune smoothing as new data arrive.

Animated reconstruction of tumor infiltration across sixteen MRI brain slices.

Scientific computing · Medical imaging

TumorPDE

A research codebase for simulating and reconstructing glioma progression on patient-specific 3D brain domains. A reaction–diffusion model describes tumor infiltration; sensitivity equations support calibration of growth, diffusion, and tumor origin from single or multiple scans.

Survival analysis · Neuroimaging

Survival modeling with image covariates

Our SMMR work uses a regularized mixture cure-rate model to distinguish susceptibility to Alzheimer’s conversion from time to conversion, with localized MRI effects estimated over irregular brain domains.

In ongoing work, we jointly model longitudinal images and interval-censored event times through functional principal components linked to a Cox model, enabling efficient estimation and inference for the overall image effect.

Estimated yeast gene regulatory network, with genes colored by cell-cycle phase and arrows showing regulatory relationships.

Dynamical systems · Sparse estimation

Differential equation models

Two papers on learning sparse dynamical systems from noisy, non-Gaussian observations. We develop estimation and structure-selection methods for high-dimensional linear ODEs and a joint estimation approach for sparse additive ODEs, with applications including yeast gene regulation.

Three axial slices showing the MNI brain template, mean annualized log-Jacobian maps of local contraction and expansion, and analysis masks.

Mini tool · MRI preprocessing

ProcessSurvADNI

A practical toolkit for downloading and preparing ADNI MRI data for imaging and survival analysis. It brings together DICOM-to-NIfTI conversion, N4 bias correction, SynthStrip skull stripping, affine and nonlinear registration, and deformation-derived log-Jacobian maps that quantify local volume change over time.

The longitudinal workflow measures change within each subject before mapping it to a common brain template.

Cover: illustrative mean of three processed annualized maps, shown with the MNI template and analysis masks.

Publications

Published or accepted

  1. Nanshan, M., Zhang, N., & Cao, J. (forthcoming). Online learning of functional principal component analysis for multidimensional functional data. Journal of the American Statistical Association, accepted. arXiv:2505.02131.
  2. Feng, J., Nanshan, M., Shi, H., Wong, K. Y., Lam, K. F., & Cao, J. (forthcoming). A regularized semiparametric cure-rate model with high-dimensional imaging data. Statistical Methods in Medical Research, accepted.
  3. Cao, J., Wu, S., Nanshan, M., Shi, H., & Wang, L. (2026). Statistical learning for functional data. Annual Review of Statistics and Its Application, 13, 149–174. doi:10.1146/annurev-statistics-042424-052503.
  4. Nanshan, M., Zhang, N., Xun, X., & Cao, J. (2022). Dynamical modeling for non-Gaussian data with high-dimensional sparse ordinary differential equations. Computational Statistics & Data Analysis, 107483. doi:10.1016/j.csda.2022.107483.
  5. Zhang, N., Nanshan, M., & Cao, J. (2022). A joint estimation approach to sparse additive ordinary differential equations. Statistics and Computing, 32, 79. doi:10.1007/s11222-022-10117-y.

Education

PhD in Statistics, Simon Fraser University — in progress

MSc in Statistics, Fudan University — 2023

BSc in Applied Mathematics, Fudan University — 2020