Below are my latest preprints on arXiv.

• A Nonparametric and Functional Wombling Methodology

  Luke A. Barratt and John A. D. Aston. July 2024. arXiv: 2502.07740

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  Wombling methods, first introduced in 1951, have been widely applied to detect boundaries and variations across spatial domains, particularly in biological, public health and meteorological studies. Traditional applications focus on finite-dimensional observations, where significant changes in measurable traits indicate structural boundaries. In this work, wombling methodologies are extended to functional data, enabling the identification of spatial variation in infinite-dimensional settings. Proposed is a nonparametric approach that accommodates functional observations without imposing strict distributional assumptions. This methodology successfully captures complex spatial structures and discontinuities, demonstrating superior sensitivity and robustness compared to existing finite-dimensional techniques. This methodology is then applied to analyse regional epidemiological disparities between London and the rest of the UK, identifying key spatial boundaries in the shape of the first trajectory of Covid-19 incidence in 2020. Through extensive simulations and empirical validation, demonstrated is the method's effectiveness in uncovering meaningful spatial variations, with potential applications in a wide variety of fields.

• Exploring Covid-19 Spatiotemporal Dynamics: Non-Euclidean Spatially Aware Functional Registration

  Luke A. Barratt and John A. D. Aston. July 2024. arXiv: 2407.17132

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  When it came to Covid-19, timing was everything. This paper considers the spatiotemporal dynamics of the Covid-19 pandemic via a developed methodology of non-Euclidean spatially aware functional registration. In particular, the daily SARS-CoV-2 incidence in each of 380 local authorities in the UK from March to June 2020 is analysed to understand the phase variation of the waves when considered as curves. This is achieved by adapting a traditional registration method (that of local variation analysis) to account for the clear spatial dependencies in the data. This adapted methodology is shown via simulation studies to perform substantially better for the estimation of the registration functions than the non-spatial alternative. Moreover, it is found that the driving time between locations represents the spatial dependency in the Covid-19 data better than geographical distance. However, since driving time is non-Euclidean, the traditional spatial frameworks break down; to solve this, a methodology inspired by multidimensional scaling is developed to approximate the driving times by a Euclidean distance which enables the established theory to be applied. Finally, the resulting estimates of the registration/warping processes are analysed by taking functionals to understand the qualitatively observable earliness/lateness and sharpness/flatness of the Covid-19 waves quantitatively.