  Understanding how genetically encoded rules drive and guide complex neuronal
growth processes is essential to comprehending the brain's architecture, and
agent-based models (ABMs) offer a powerful simulation approach to further
develop this understanding. However, accurately calibrating these models
remains a challenge. Here, we present a novel application of Approximate
Bayesian Computation (ABC) to address this issue. ABMs are based on
parametrized stochastic rules that describe the time evolution of small
components -- the so-called agents -- discretizing the system, leading to
stochastic simulations that require appropriate treatment. Mathematically, the
calibration defines a stochastic inverse problem. We propose to address it in a
Bayesian setting using ABC. We facilitate the repeated comparison between data
and simulations by quantifying the morphological information of single neurons
with so-called morphometrics and resort to statistical distances to measure
discrepancies between populations thereof. We conduct experiments on synthetic
as well as experimental data. We find that ABC utilizing Sequential Monte Carlo
sampling and the Wasserstein distance finds accurate posterior parameter
distributions for representative ABMs. We further demonstrate that these ABMs
capture specific features of pyramidal cells of the hippocampus (CA1). Overall,
this work establishes a robust framework for calibrating agent-based neuronal
growth models and opens the door for future investigations using Bayesian
techniques for model building, verification, and adequacy assessment.
