Optimal Bayesian Designs for Detecting Temporal and Spatio-temporal Changes in Ecological Systems Using Mean Field Variational Bayes
Conference
Format: IPS Abstract
Keywords: ecological monitoring, evidence lower bound, generalised additive mixed models, hard coral cover, high-dimensional data, spatio-temporal change detection, spatio-temporal models, temporal change detection
Session: Invited Session 7B - Advanced Statistical Approaches to Coral Reef Modelling and Monitoring
Wednesday 4 December 9:30 a.m. - 11 a.m. (Australia/Adelaide)
Abstract
Bayesian spatio-temporal designs have become indispensable tools for analysing data that vary across both space and time, particularly in ecological monitoring. These designs enable the incorporation of prior knowledge and the dynamic updating of beliefs as new data emerge, making them highly adaptable to changing environments. Despite their advantages, the practical application of Bayesian spatio-temporal designs is often hindered by challenges related to high dimensionality and computational complexity, limiting their real-world usability.
This study addresses these challenges by presenting a model-based Bayesian design framework that employs Mean Field Variational Bayes (MFVB) to optimally capture temporal and spatio-temporal changes in complex ecological systems. MFVB offers a substantial computational advantage over the frequently used Laplace approximation by more efficiently approximating posterior distributions during utility evaluations, which is particularly advantageous in high-dimensional settings.
Our methodology is applied to the ecological monitoring of shoals in Western Australia, to detect changes in hard coral cover across space and time. Two models are employed: one to capture overall temporal changes and another to detect spatio-temporal variations. Both models are constructed within the Generalised Additive Mixed Modelling (GAMM) framework, known for its robustness in handling model uncertainty. Bayesian model selection, guided by the Evidence Lower Bound (ELBO), ensures that the best-fitting model informs our Bayesian designs.
The study develops two types of Bayesian designs: one tailored to capture consistent temporal changes and another aimed at detecting variations at specific spatial locations over time. The utility functions developed to quantify these designs ensure accurate and precise detection of these two distinct types of change. By optimising these utility functions, we strategically identify designs that effectively capture temporal and spatio-temporal changes in hard coral cover at the Barracouta East shoal in Western Australia.
Our results demonstrate that the proposed designs are highly effective for monitoring ecological systems, providing a robust and computationally efficient solution for detecting changes in hard coral cover. These designs offer significant potential for broader applications in environmental monitoring and management.