A Bayesian inference approach to account for multiple sources of uncertainty in a macroalgae based integrated multi-trophic aquaculture model

A Bayesian inference method was employed to quantify uncertainty in an Integrated Multi-Trophic Aquaculture (IMTA) model. A deterministic model was reformulated as a Bayesian Hierarchical Model (BHM) with uncertainty in the parameters accounted for using “prior” distributions and unresolved time varying processes modelled using auto-regressive processes. Observations of kelp grown in 3 seeding densities around salmon pens were assimilated using a Sequential Monte Carlo method implemented within the LibBi package. This resulted in a considerable reduction in the variability in model output for both the observed and unobserved state variables. A reduction in variance between the prior and posterior was observed for a subset of model parameters which varied with seeding density. Kullback-Liebler (KL) divergence method showed the reduction in variability of the state and parameters was approximately 90%. A low to medium seeding density results in the most efficient removal of excess nutrients in this simple system.