| Scientists use complex deterministic models to study and forecast the behavior of a variety of physical and biological processes, with increasing emphasis on incorporating data to inform model input parameters and accounting for parameter uncertainty. One approach to this data-model integration utilizes Bayesian statistical methods, to which the deterministic model can pose a challenge. We describe the development of Bayesian parameter estimation for two applications. In the first application, we develop reversible jump Markov chain Monte Carlo sampling-with the novelty of a continuous model index-for the input parameters of an individual-based model of tree growth and mortality, which is under development to explore forest dynamics and tree responses to environmental drivers. Results are comparable with a non-reversible jump approach but our reversible jump approach may be preferable when scaling up to big data sets. In the second, we investigate the effect of numerical instability of discretized partial differential equation diffusion models in a hierarchical Bayesian framework. |
