We are investigating simple linear factor analysis models of gene regulation in which transcription factor proteins are treated as
latent variables. An informative prior on the regulatory network enforces sparsity in these models. Previously we have exploited
variational methods to perform approximate Bayesian inference over continuous-valued model parameters and time-correlated latent variables. However, when also carrying out inference over the binary network parameters a naive mean-field variational approximation does not allow us to explore the multiple modes in the posterior distribution. I will describe recent work exploiting the sparsity of solutions in order to develop efficient Gibbs sampling strategies that are practical for inference over high-dimensional matrices.