A molecular interaction library modeling favorable non-bonded interactions between atoms and molecular fragments is considered. In this paper, we represent the structure of the interaction library by a network diagram, which demonstrates that the underlying prediction model obtained for a molecular fragment is multi-layered. We clustered the molecular fragments into four groups by analyzing the pairwise distances between the molecular fragments. The distances are represented as an unrooted tree, in which the molecular fragments fall into four groups according to their function. For each fragment group, we modeled a group-specific a priori distribution with a Dirichlet distribution. The group-specific Dirichlet distributions enable us to derive a large population of similar molecular fragments that vary only in their contact preferences. Bayes' theorem then leads to a population distribution of the posterior probability vectors referred to as a "Dickey-Savage"-density. Two known methods for approximating multivariate integrals are applied to obtain marginal distributions of the Dickey-Savage density. The results of the numerical integration methods are compared with the simulated marginal distributions. By studying interactions between the protein structure of cyclohydrolase and its ligand guanosine-5'-triphosphate, we show that the marginal distributions of the posterior probabilities are more informative than the corresponding point estimates.