Abstract:

 

In this talk, we describe a Markov chain Monte Carlo (MCMC) algorithm for estimating the input parameters of an individual-based model (IBM) of tree growth. Some input values of the IBM lead to output values that are discordant with observed tree mortality, i.e., the IBM deterministically kills trees it shouldn't, or vice-versa. In such discordant cases, we introduce stochastic tree quantities (e.g., heights), which would otherwise be determined by the IBM if not for the discordance. As a result, the dimension on unknown quantities in the estimation problem depends on the IBM inputs. Traditional MCMC algorithms (e.g., Metropolis-Hastings (MH)) cannot accommodate such changes in dimension, and we are led to consider a reversible jump algorithm (RJMCMC) to handle trans-dimensional moves through the space of unknown quantities. We discuss the MH algorithm and its extension to the reversible jump algorithm, illustrating RJMCMC in a simple example of regression model choice, where changes in parameter space dimension are easily seen to arise from the changing numbers of regressor variables in the regression model. This regression model choice example is typical of the vast majoring of applications of RJMCMC, wherein there is a finite or countable number of models (each model in the model choice example is just a typical regression model with a few regression function parameters). We describe the RJMCMC algorithm applied to our IBM estimation problem, and discuss how our application of RJMCMC is relatively unique in that our "models" are indexed by the IBM input values, which reside in an uncountable space. We also discuss how our algorithm's moves between spaces of differing dimension do not afford the intuition to construct moves compared to more typical applications of RJMCMC.