I just arXived the final version of our technical note “Approximate Bayesian parameterization of a process-based tropical forest model” (coauthored with Claudia Dislich, Thorsten Wiegand and Andreas Huth) that is now accepted and will appear in Biogeosciences soon. There have been a few minor changes in response to reviewer comments on a discussion version of this paper that was also published by Biogeosciences and that I blogged about last year.
To give you the story in a nutshell: if you have any stochastic simulation and you want to fit this simulation to data, you can use the stochasticity of your model outputs to create an approximation for the probability of obtaining the data you observed conditional on your model / parameters, and you can then use this probability (Likelihood) to compare different models and parameters (see our 2011 review in EL). One popular way to do this is Approximate Bayesian Computation (ABC), which I explained with an example in a recent post. Another option is the method of synthetic likelihoods used by Wood, Nature 2010. The idea of the latter method is that you run the stochastic model many times, fit a distribution to the model outputs, and compare the probability density of this distribution to your data to get the likelihood. We called this a “parametric approximation” in our review, which still seems a more appropriate name to me, but I guess the term “synthetic likelihood” is more well known now and sticks for the moment.
What we show in the paper is that the method of synthetic likelihoods works pretty well to fit a comparatively complex forest model to data. It does sound rather trivial, but I have to admit that I was quite surprised that this works so well, I didn’t expect this when we started this project, and it’s to my knowledge the first application of such a method to rather complex ecological model.
Among other things, I see this paper as an encouragement for ecological modelers to try this method out. Synthetic likelihoods, although noted by statisticians and the ABC crowd, are still pretty much undiscovered by the larger ecological modeling community (as is ABC, although to a lesser extent), which is unfortunate because these approaches offer a tremendous potential to embed simulation models much tighter in empirical data.
Addition: a pdf of the final paper is here.