For Bayesian inference on the mixture of factor analyzers, natural conjugate priors on the parameters are introduced, and then a Gibbs sampler that generates parameter samples following the posterior is constructed. In addition, a deterministic estimation algorithm is derived by taking modes instead of samples from the conditional posteriors used in the Gibbs sampler. This is regarded as a maximum a posteriori estimation algorithm with hyperparameter search. The behaviors of the Gibbs sampler and the deterministic algorithm are compared on a simulation experiment.