Subhash Lele
Modeling population dynamics is essential to study ecological populations whether for maintaining the existing populations (e.g. Population Viability Analysis) or for controlling spread of invasive species. Meta-population dynamics that takes into account of immigration and emigration also plays an important role in studying spread of invasive species. Systems of ordinary differential equations are used to model growth and spread of forest insects and pests. Many of these processes evolve in continuous time and space but the data are obtained only at discrete times and discrete locations and with measurement error. Hierarchical models are a convenient way to model such imperfectly and partially observed processes.
Statistical inference for such models poses significant computational difficulties. In this paper, I review data cloning (Lele et al. 2007), a simple computational method that exploits advances in Bayesian computation, in particular the Markov Chain Monte Carlo method, to conduct statistical inference for hierarchical models. This includes (i) parameter estimation, (ii) confidence intervals, (iii) model selection, and (iv) forecasting future states and the uncertainty associated with such forecasts.
One of the basic tenets of good modeling is that complexity of the model should not exceed information in the data. The mismatch in the two can lead to parameter non-estimability. Determining estimability of the parameters in a hierarchical model is, in general, a very difficult problem. Data cloning provides a simple graphical test to not only check if the full set of parameters is estimable but also, and perhaps more importantly, if a specified function of the parameters is estimable.
I will illustrate data cloning in 1) Population Viability Analysis in the presence of measurement error, 2) Two species Leslie-Gower Competition model, and 3) Analysis of systems of differential equations arising in epidemiology and ecology.
