Reversible jump MCMC for inference in a deterministic individual-based model of tree growth for studying forest dynamics

Scientists use deterministic models to study and forecast the behavior of complex environmental processes, with increasing emphasis on incorporating data to inform model input parameters and accounting for parameter uncertainty. We work with a deterministic, individual-based model (IBM) of tree growth and mortality, which is under development to explore forest dynamics. Some values of IBM input parameters cause premature virtual tree mortality relative to the actual mortality status of an observed tree. This discordance in mortality causes dimension changes in the state of a stochastic implementation of IBM outputs and leads us to address trans-dimensional moves among states with a novel formulation of reversible jump Markov chain Monte Carlo (RJMCMC). In particular, we present an RJMCMC algorithm that uses a continuously supported, multidimensional index-the IBM input parameter-instead of a discrete index typical of model determination applications. We use both synthetic data and data from the Forest Inventory and Analysis database representing two tree species. We compare results for each dataset and species between our reversible jump (RJ) specification and an alternative, non-RJ specification. The RJ formulation compares favorably to the non-RJ formulation with regard to achieving convergence and yielding biologically realistic IBM input parameter estimates.