36,864 research outputs found
A hybrid sampler for Poisson-Kingman mixture models
This paper concerns the introduction of a new Markov Chain Monte Carlo scheme
for posterior sampling in Bayesian nonparametric mixture models with priors
that belong to the general Poisson-Kingman class. We present a novel compact
way of representing the infinite dimensional component of the model such that
while explicitly representing this infinite component it has less memory and
storage requirements than previous MCMC schemes. We describe comparative
simulation results demonstrating the efficacy of the proposed MCMC algorithm
against existing marginal and conditional MCMC samplers
Bayesian nonparametric Plackett-Luce models for the analysis of preferences for college degree programmes
In this paper we propose a Bayesian nonparametric model for clustering
partial ranking data. We start by developing 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 completely random measure. We characterise the
posterior distribution given data, and derive a simple and effective Gibbs
sampler for posterior simulation. We then develop a Dirichlet process mixture
extension of our model and apply it to investigate the clustering of
preferences for college degree programmes amongst Irish secondary school
graduates. The existence of clusters of applicants who have similar preferences
for degree programmes is established and we determine that subject matter and
geographical location of the third level institution characterise these
clusters.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS717 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Consistency of Markov chain quasi-Monte Carlo on continuous state spaces
The random numbers driving Markov chain Monte Carlo (MCMC) simulation are
usually modeled as independent U(0,1) random variables. Tribble [Markov chain
Monte Carlo algorithms using completely uniformly distributed driving sequences
(2007) Stanford Univ.] reports substantial improvements when those random
numbers are replaced by carefully balanced inputs from completely uniformly
distributed sequences. The previous theoretical justification for using
anything other than i.i.d. U(0,1) points shows consistency for estimated means,
but only applies for discrete stationary distributions. We extend those results
to some MCMC algorithms for continuous stationary distributions. The main
motivation is the search for quasi-Monte Carlo versions of MCMC. As a side
benefit, the results also establish consistency for the usual method of using
pseudo-random numbers in place of random ones.Comment: Published in at http://dx.doi.org/10.1214/10-AOS831 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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