BayeSpace - Applying Bayesian Statistics to Environmental and Ecological Phenomena

Abstract

Environmental and ecological phenomena are inherently complex, dynamic, and uncertain — requiring analytical tools that can generate accurate predictions while transparently quantifying uncertainty. This thesis introduces BayeSpace, a modular Python framework for applying Bayesian inference to spatiotemporal environmental and ecological modelling. It addresses key limitations in existing approaches, including fragmented workflows, steep learning curves, and model visualisation and comparison.

BayeSpace integrates two core Bayesian methodologies: Bayesian Regression (BR) for problems with known functional forms, and Gaussian Process Regression (GPR) for flexible, non-parametric modelling. Built on libraries such as NumPyro and scikit-learn, it provides core classes for model definition, prior and likelihood specification, sampling, and visualisation. Key innovations include automated experiment tracking, domain generation, data simulation, kernel and transformation flexibility, and robust visualisation tools.

The framework's capabilities are demonstrated through several applications. In marine cloud brightening research, BR was used to infer atmospheric dispersion parameters from real-world plume data over the Great Barrier Reef, suggesting oceanic dispersion may be more intense than terrestrial models predict. This case study illustrates BayeSpace's ability to explore complex phenomena, identify model limitations, and understand asymptotic behaviour. In species distribution modelling, GPR effectively handled spatiotemporal occurrence data, with model performance strongly correlating with total grid coverage. BayeSpace's iteration ability and flexibility were vital in designing a one-size-fits-all framework for species distribution modelling.

Validation using simulated and real-world datasets confirmed BayeSpace's accuracy in linear cases while revealing challenges in highly non-linear regimes where complex posteriors affect sampler convergence.