Inference for Bayesian Nonparametric Models with Binary Response Data via Permutation Counting

Since the beginning of Bayesian nonparametrics in early 1970s, there has been a wide interest constructing models for binary response data. Such data arise naturally problems dealing with bioassay, current status and sensitivity testing, are equivalent to left right censored observations if inputs one-dimensional. For based on Dirichlet process, inference is possible via Markov chain Monte Carlo (MCMC) simulations. However, exist multiple processes different principles, which such MCMC-based methods fail. Examples include logistic Gaussian quantile pyramids. These require MCMC posterior given exact observations, thus become intractable when comprise both observations. Here we present new importance sampling algorithm nonparametric exchangeable It can be applied any model from samples generated, or even only approximately generated. The main idea behind exploit symmetries introduced by exchangeability. Calculating weights turns out evaluating permanent certain class (0,1)-matrix, prove done polynomial time deriving an explicit algorithm.