By expressing prior distributions as general stochastic processes,
nonparametric Bayesian methods provide a flexible way to incorporate prior
knowledge and constrain the latent structure in statistical inference. The
Indian buffet process (IBP) is such an example that can be used to define a
prior distribution on infinite binary features, where the exchangeability among
subjects is assumed. The phylogenetic Indian buffet process (pIBP), a
derivative of IBP, enables the modeling of non-exchangeability among subjects
through a stochastic process on a rooted tree, which is similar to that used in
phylogenetics, to describe relationships among the subjects. In this paper, we
study the theoretical properties of IBP and pIBP under a binary factor model.
We establish the posterior contraction rates for both IBP and pIBP and
substantiate the theoretical results through simulation studies. This is the
first work addressing the frequentist property of the posterior behaviors of
IBP and pIBP. We also demonstrated its practical usefulness by applying pIBP
prior to a real data example arising in the field of cancer genomics where the
exchangeability among subjects is violated