  Density-functional theory is widely used to predict the physical properties
of materials. However, it usually fails for strongly correlated materials. A
popular solution is to use the Hubbard corrections to treat strongly correlated
electronic states. Unfortunately, the exact values of the Hubbard $U$ and $J$
parameters are initially unknown, and they can vary from one material to
another. In this semi-empirical study, we explore the $U$ and $J$ parameter
space of a group of iron-based compounds to simultaneously improve the
prediction of physical properties (volume, magnetic moment, and bandgap). We
used a Bayesian calibration assisted by Markov chain Monte Carlo sampling for
three different exchange-correlation functionals (LDA, PBE, and PBEsol). We
found that LDA requires the largest $U$ correction. PBE has the smallest
standard deviation and its $U$ and $J$ parameters are the most transferable to
other iron-based compounds. Lastly, PBE predicts lattice parameters reasonably
well without the Hubbard correction.
