A Bayesian approach to state and parameter estimation in a Phytoplankton-Zooplankton model

Complex marine biogeochemical (BGC) models are now being used to inform management decisions at a variety of scales, from local coastal management issues through to the global effects of climate change. A majority of BGC models are still deterministic in nature with model tuning and calibration performed in a heuristic manner. This method does not allow for a quantitative estimate of model or parameter uncertainty. If these models are reformulated in a physical-statistical framework, using a stochastic process model, formal state and parameter estimation routines can be implemented, yielding quantitative estimates of model uncertainty. We have performed twin experiments using an idealised stochastic-dynamic non-linear phytoplankton-zooplankton model to trial two Markov Chain Monte Carlo (MCMC) Algorithms. The first uses a Particle Filter (PF) with a Metropolis-Hastings (MH) update step for state-estimation embedded within a MH MCMC for hyper-parameter estimation; we have named this approach MH-PF-MH. The second approach uses Gibbs sampling for state estimation and MH MCMC over hyper-parameters; referred to as MH-Gibbs. Both algorithms performed well in the twin-experiments, allowing both state and parameter estimation. The hybrid MH-Gibbs is more efficient than the MH-PF-MH algorithm, forming a reliable posterior sample with up to 99.9% fewer model trajectories. However, the MH-PF-MH algorithm is expected to be more flexible in its implementation.