  While the usual goal in Monte Carlo (MC) simulations of Ising models is the
efficient generation of spin configurations with Boltzmann probabilities, the
inverse problem is to determine the coupling constants from a given set of spin
configurations. Most recent work has been limited to local magnetic fields and
pair-wise interactions. We have extended solutions to multi-spin interactions,
using correlation function matching (CFM). A more serious limitation of
previous work has been the uncertainty of whether a chosen set of interactions
is capable of faithfully representing real data. We show how our confirmation
testing method uses an additional MC simulation to detect significant
interactions that might be missing in the assumed representation of the data.
