Rigorous and expansive biological experiments of genes involve not only multiple replicates of sparse time data developed within a given laboratory but also, potentially, replicates generated by multiple laboratories. The posterior probability of a directed acyclic graph (DAG) of our models of gene associations given the hierarchical time-course data is proportional to the product of the prior probability of the DAG and the likelihood of the data given the DAG. From such data modeling, protein or gene interaction posterior probabilities are computed based on hierarchical structures. A result based on multiple replicates in a single laboratory is developed first, then extended it to replicates from multiple laboratories. Rather than assuming equal priors for DAGs, three methods to estimate the prior probabilities of DAGs are presented. Their sensitivity based on different assumptions and additional information are discussed here. At the same time, the odds ratio of two estimates under the same setting are calculated. The odds ratio often has a much more concise form and is easier to apply in practical computations than the priors themselves.