[School of Natural Sciences PhD Scholarships] Analysis of Spatial Time Series Data using Random Matrices

The challenge

Modern monitoring systems generate spatial time series (STS): measurements collected over many time points at many locations, producing “large p, large T” data matrices. Classical methods struggle with such scale and complexity. This project will develop new Random Matrix Theory (RMT)-based tools to uncover structure, quantify uncertainty, and enable reliable inference in high-dimensional STS.

Project objectives

You will develop RMT-driven methodology to:

• Identify space–time dependency structures in massive STS datasets.
• Estimate large space–time covariance and precision matrices with theoretical guarantees.
• Test hypotheses about dependence, separability, and variability in the “large p, large T” regime.

Methods you will use and develop

You will model STS as sequences of high-dimensional random matrices and exploit asymptotic spectral laws (such as Marchenko–Pastur limits and linear spectral statistics) to build data-driven diagnostics of space–time structure. Your toolkit will include:

• Spectral analysis of sample space–time covariance and autocovariance matrices under dependence and mild nonstationarity.
• Regularized estimation via shrinkage, tapering, and sparse graphical models guided by RMT.
• Eigenvalue-based tests for space–time independence, separability, and covariance homogeneity.
• Space–time factor models with RMT-based selection tools.

Computationally, you will implement scalable algorithms (composite likelihood, spectral methods, low-dimensional approximations) in R/Python, leveraging high-performance computing.

Expected outcomes

By the end of the PhD you might be producing:

• New RMT-based estimators and tests for large space–time covariance structures, with provable properties.
• Open-source software that makes these methods usable by practitioners.
• Applied case studies in at least two domains (for example, climate reanalysis and epidemiological panels), showing improved dependency discovery, forecasting, and anomaly detection over existing spatio-temporal models.

Supervision, training, and environment

You will be co-supervised by experts in high-dimensional statistics and spatio-temporal modelling, with regular meetings and milestone-driven reviews. Your training will include advanced courses in mathematics, probability, and spatio-temporal statistics; workshops on scalable computation and reproducible research; and hands-on experience with university high-performance computing.

You will join an active research group, present regularly at seminars. You will receive dedicated writing support for papers and your thesis, with opportunities for co-authorship on methodological and applied publications.

For more information, please contact Madhu Bhattacharjee and/or Arup Bose (Indian Statistical Institute, Kolkata, India)

Career prospects

By graduation, you will have a compelling portfolio of theoretical results, software contributions, and real-world applications, positioning you for roles in academia, data science, or quantitative industries such as finance, tech, and climate analytics.

This project is expected to start in September 2027.

Before you apply: We strongly recommend that you contact the supervisors for this project before you apply.

How to apply: To be considered for this project you must complete a formal application through our online application portal. If you already have an applicant account this link will directly open an application for PhD School of Natural Sciences Scholarships. If you don’t already have an applicant account, please follow the instructions here.

When applying, please specify the full title and supervisor/s of the project, details of your previous study, and names and contact details of two referees. You must also upload a Supporting Statement describing your motivation to apply to the project, your CV and transcripts of awarded and in-progress university qualifications. Please note late or incomplete applications will not be considered.

Equality, diversity and inclusion are fundamental to the success of The University of Manchester and central to all our activities. A diverse research community strengthens creativity, productivity and quality, while increasing the societal and economic impact of our work. We welcome applicants from all career paths, backgrounds and sections of the community, regardless of age, disability, ethnicity, gender, gender expression, sexual orientation or transgender status.

We welcome applications from candidates returning to study after a career break or experience in other roles. Flexible study arrangements may be available, including part-time study at 50%, 60% or 80%, subject to the requirements of the project and funder.

Eligibility: The standard academic entry requirement for this PhD is an upper second-class (2:1) honours degree (or international equivalent) in Statistics, Mathematics, or allied areas OR any upper-second class (2:1) honours degree and a Master’s degree at merit (or international equivalent) in Statistics, Mathematics, or allied areas. Skill in R programming (substantiated by curriculum taken and/or projects) is desired, along with evidence of interest in research, and experience in (statistical) modelling and analysis of spatio-temporal data.

This project will remain open until filled.

If your application is submitted by 1st November 2026, you can expect a decision by 18th December 2026.

If your application is submitted by 15th January 2027, you can expect a decision by 30th March 2027.

Self or externally funded students can also be considered for this project.

FSE_SoNS

Funding Notes

Funding covers tuition fees, an annual stipend at the UKRI minimum rate (currently £21,805 per year), and a research training support grant of up to £2,500 per year for the full 3.5-year programme.