I've just posted this paper to arXiv (full resolution version here, but be warned, it' about 180Mb), which is the first in a series that attempts to carefully explore constraints on Galacticus from observations of the galaxy population.

In this paper, I use an extremely simple galaxy formation model, and a single constraint - the z=0 stellar mass function of galaxies. What sets this study apart from previous, similar studies, is that I attempt to carefully quantify sources of random and systematic error in both the data and the model, and to account for these when constructing the model likelihood function. For example, I compute the full covariance matrix of the stellar mass function, which turns out to look like this (well, technically this is the correlation matrix):

The result is that a good match to the z=0 stellar mass function can be obtained, along with a moderately good "prediction" (which is really an extrapolation) of the evolution of the stellar mass function to z=1. Other statistics, such as the HI mass function of galaxies at z=0, don't work out as well.

Accounting for all sources of random and systematic error significantly broadens the posterior distributions on model parameters - which is important if we want to avoid ruling out viable models. Ignoring these errors also leads to discernable biases in the parameter posteriors.

This is just step one in constructing a data-driven, robustly constrained galaxy formation model. Work on step two is already underway.......