Just so you know, the Latent Dirichlet Allocation is very much a Bayesian model, as it says in the original paper's abstract [1] (first google hit).

(LDA is a bit of an overloaded acronym in machine learning, but I'm assuming that's what you mean.)

[1] http://www.cs.princeton.edu/~blei/papers/BleiNgJordan2003.pd...