Background

• multiple pollutant components of PM2.5 globally

• highly multivariate

• large spatial scale

• asymmetric cross-covariance

Methodological innovations

• developed a hybrid spatial graph model framework

• introduced auto-/ cross-neighbourhood 

• innovated cross-Markov Random Field  (cross-MRF) theory

• developed step-wise parallel algorithms that construct the desired joint covariance matrix and joint precision matrix concurrently in each step

• explored co-existence of geostatistical and MRF modelling approaches in one unified framework (an open problem)

Impacts

• provide the sparsest possible representation of the joint precision matrix, with 

  • • the highest possible exact-zero-value percentage

    • the lowest possible joint precision matrix generation order 

    • the fastest possible generation speed 

• provide a potential solution to an open problem

Background

• Multivariate spatial phenomena are ubiquitous, spanning climate, pandemics, air quality, and social economy domains

• Cross-correlation between different quantities of interest at various locations is asymmetric in general

Contributions

• This paper provides the visualisation, structure, and properties of asymmetric cross-correlation as well as symmetric auto-correlation

• It illustrates the difference in model accuracy with and without asymmetric accommodation using a 1D simulated example

Background

• Matern correlation is of pivotal importance in machine learning

Contributions

• This paper focuses on the exposition of its changing behaviour and smoothness properties in response to the change of its two parameters

• It is illustrated with a series of simulation studies, the use of an interactive 3D visualisation applet, and a practical modelling example

• Provided a pragmatic guide for researchers in their real-world modelling endeavours, such as setting appropriate initial values for these parameters and parameter-fine-tuning in their Bayesian modelling or simulation studies 

Method

• Used a stochastic SEIR network model to conduct scenario simulations under different UK COVID-19 policies 

Contributions

• Provided first-hand evidence for the development of the NHS COVID-19 App led by Turing fellow Professor Mark Briers

Methods

• Developed a Bayesian hierarchical spatial model to estimate PM2.5 concentrations across London at the aggregated local authority level

• Quantified the uncertainties for these areal-aggregated estimates from point-level model outputs using Ordinary Monte Carlo, Markov Chain Monte Carlo, and theoretical reasoning

• Quantified and 3-D visualise the non-compliance probabilities of exceeding the WHO’s PM2.5 compliance limit within each local authority

Impact

• • • Support policymakers in making more informed decisions on environmental protection and air pollution control