  Inverse parameter estimation of process-based models is a long-standing
problem in many scientific disciplines. A key question for inverse parameter
estimation is how to define the metric that quantifies how well model
predictions fit to the data. This metric can be expressed by general cost or
objective functions, but statistical inversion methods require a particular
metric, the probability of observing the data given the model parameters, known
as the likelihood.
  For technical and computational reasons, likelihoods for process-based
stochastic models are usually based on general assumptions about variability in
the observed data, and not on the stochasticity generated by the model. Only in
recent years have new methods become available that allow the generation of
likelihoods directly from stochastic simulations. Previous applications of
these approximate Bayesian methods have concentrated on relatively simple
models. Here, we report on the application of a simulation-based likelihood
approximation for FORMIND, a parameter-rich individual-based model of tropical
forest dynamics.
  We show that approximate Bayesian inference, based on a parametric likelihood
approximation placed in a conventional Markov chain Monte Carlo (MCMC) sampler,
performs well in retrieving known parameter values from virtual inventory data
generated by the forest model. We analyze the results of the parameter
estimation, examine its sensitivity to the choice and aggregation of model
outputs and observed data (summary statistics), and demonstrate the application
of this method by fitting the FORMIND model to field data from an Ecuadorian
tropical forest. Finally, we discuss how this approach differs from approximate
Bayesian computation (ABC), another method commonly used to generate
simulation-based likelihood approximations.
  Our results demonstrate that simulation-based inference, [...]
