A wide variety of priors have been proposed for nonparametric Bayesian estimation of conditional distributions, and there is a clear need for theorems providing conditions on the prior for large support, as well as posterior consistency. Estimation of an uncountable collection of conditional...

We define a class of reinforced urn processes, based on Hoppe’s urn scheme, that are Markov exchangeable, with a countable and possibly unknown state space. This construction extends the reinforced urn processes developed by Muliere et al. (2000) and widely used in Bayesian nonparametric...

We propose a mixed multinomial logit model, with the mixing distribution assigned a general (nonparametric) stick-breaking prior. We present a Markov chain Monte Carlo (MCMC) algorithm to sample and estimate the posterior distribution of the model’s parameters. The algorithm relies on a Gibbs...

This paper uses an infinite hidden Markov model (IIHMM) to analyze U.S. inflation dynamics with a particular focus on the persistence of inflation. The IHMM is a Bayesian nonparametric approach to modeling structural breaks. It allows for an unknown number of breakpoints and is a flexible and...

This introduction to Bayesian statistics presents the main concepts as well as the principal reasons advocated in favour of a Bayesian modelling. We cover the various approaches to prior determination as well as the basis asymptotic arguments in favour of using Bayes estimators. The testing...

We consider the consistency of the Bayes factor in goodness of fit testing for a parametric family of densities against a non-parametric alternative. Sufficient conditions for consistency of the Bayes factor are determined and demonstrated with priors using certain mixtures of triangular densities.