1,834 research outputs found
Bayesian nonparametric models for ranked data
We develop a Bayesian nonparametric extension of the popular Plackett-Luce
choice model that can handle an infinite number of choice items. Our framework
is based on the theory of random atomic measures, with the prior specified by a
gamma process. We derive a posterior characterization and a simple and
effective Gibbs sampler for posterior simulation. We develop a time-varying
extension of our model, and apply it to the New York Times lists of weekly
bestselling books.Comment: NIPS - Neural Information Processing Systems (2012
A Bayes method for a monotone hazard rate via S-paths
A class of random hazard rates, which is defined as a mixture of an indicator
kernel convolved with a completely random measure, is of interest. We provide
an explicit characterization of the posterior distribution of this mixture
hazard rate model via a finite mixture of S-paths. A closed and tractable Bayes
estimator for the hazard rate is derived to be a finite sum over S-paths. The
path characterization or the estimator is proved to be a Rao--Blackwellization
of an existing partition characterization or partition-sum estimator. This
accentuates the importance of S-paths in Bayesian modeling of monotone hazard
rates. An efficient Markov chain Monte Carlo (MCMC) method is proposed to
approximate this class of estimates. It is shown that S-path characterization
also exists in modeling with covariates by a proportional hazard model, and the
proposed algorithm again applies. Numerical results of the method are given to
demonstrate its practicality and effectiveness.Comment: Published at http://dx.doi.org/10.1214/009053606000000047 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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