We develop a Bayesian Iterated Learning Model (BILM) that models the cultural evolution of language as it is transmitted over generations of learners. We study the outcome of iterated learning in relation to the behavior of individual agents (their biases) and the social structure through which they transmit their behavior. BILM makes individual learning biases explicit and offers a direct comparison of how individual biases relate to the outcome of iterated learning. Most earlier BILMs use simple one parent to one child (monadic) chains of homogeneous learners to study the outcome of iterated learning in terms of bias manipulations. Here, we develop a BILM to study two novel manipulations in social parameters: population size and population heterogeneity, to determine more precisely what the transmission process itself can add to the outcome of iterated learning. Our monadic model replicates the existing BILM results, however our manipulations show that the outcome of iterated learning is sensitive to more factors than are explicitly encoded in the prior. This calls into question the appropriateness of assuming strong Bayesian inference in the iterated learning framework and has important implications for the study of language evolution in general.