We apply Bayesian data analysis to a structured cognitive model in order to determine the priors that support human generalizations in a simple concept learning task. We modeled 250,000 ratings in a "number game" experiment where subjects took examples of a numbers produced by a program (e.g. 4, 16, 32) and rated how likely other numbers (e.g. 8 vs. 9) would be to be generated. This paper develops a data analysis technique for a family of compositional "Language of Thought" (LOT) models which permits discovery of subjects' prior probability of mental operations (e.g. addition, multiplication, etc.) in this domain. Our results reveal high correlations between model mean predictions and subject generalizations, but with some qualitative mismatch for a strongly compositional prior.