Model-robust Bayesian design through generalised additive models for monitoring submerged shoals

Abstract

Optimal sampling strategies are critical for surveys of deeper coral reef and shoal systems due to the significant cost of accessing and field sampling these remote and poorly understood ecosystems. Additionally, well-established standard diver-based sampling techniques used in shallow reef systems are not feasible at greater depths. In this study, we develop a Bayesian design strategy to optimise sampling for a shoal deep reef system using three years of pilot data. Bayesian designs are typically found by maximising the expectation of a utility function with respect to the joint distribution of the parameters and the response conditional on an assumed statistical model. Unfortunately, specifying such a model a priori is difficult, as knowledge of the data-generating process is typically incomplete. To overcome this, our approach focuses on finding Bayesian designs that are robust to unknown model uncertainty. We achieve this by couching the specified model within a generalised additive modelling framework and formulating prior information that allows the additive component to capture discrepancies between what is assumed and the underlying data-generating process. The motivation for this is to enable Bayesian designs to be found under epistemic model uncertainty; a highly desirable property of Bayesian designs. Initially, we demonstrate our approach with an exemplar design problem, deriving a theoretical result to explore the properties of optimal designs. We then apply this approach to design future monitoring of submerged shoals off the north-west coast of Australia to improve current monitoring practices.