We propose two Markov chain Monte Carlo (MCMC) methods for Bayesian inference via propositionalized probability computation using binary decision diagrams (BDDs). The main advantage of our methods is that it has no restriction on logical formulas. To illustrate our methods, we first formulate LDA (latent Dirichlet allocation) which is a well-known generative probabilistic model for bag-of-words as a form of statistical abduction, and compare the learning result of our methods with that of an MCMC method called collapsed Gibbs sampling specialized for LDA. We also apply our methods to two problems, one is diagnosis for failure in a logic circuit and the other is evaluating abductive hypotheses for metabolic pathway. The experiment results show Bayesian inference using proposed methods achieves better accuracy than that of Maximum likelihood estimation.