Abstract: In non-negtive matrix factorization (NMF), a data matrix is modelled as the product of two matrices with non-negative entries. Taking a Bayesian approach to NMF entails specifying an appropriate likelihood and priors for the factorizing matrices and the number of components, K. Related to Bayesian NMF is also models based on the Indian buffet process. For a given value of K, inference can be performed using standard methods such as Gibbs sampling or variational approximation; however, infering K is more challenging. Computationally expensive approaches including Chib's method, thermodynamic integration, and reversible jump independence MCMC have been proposed.