The performance of a diagnostic test is best evaluated against a reference test that is without
error. For many diseases, this is not possible, and an imperfect reference test must be used …

Weak Convergence Page 1 1.3 Weak Convergence In this section IDl and IE are metric spaces
with metrics d and e, respectively. The set of all continuous, bounded functions f: IDl 1--+ IR is …

ABSTRACT A natural Bayesian approach for mixture models with an unknown number of
components is to take the usual finite mixture model with symmetric Dirichlet weights, and …

Ensembles of decision trees are a useful tool for obtaining flexible estimates of regression
functions. Examples of these methods include gradient-boosted decision trees, random …

We consider the asymptotic behavior of posterior distributions and Bayes estimators based
on observations which are required to be neither independent nor identically distributed. We …

We derive rates of contraction of posterior distributions on nonparametric or semiparametric
models based on Gaussian processes. The rate of contraction is shown to depend on the …

In this paper, I review the main results on the asymptotic properties of the posterior
distribution in nonparametric or high-dimensional models. In particular, I explain how …

This paper studies convergence behavior of latent mixing measures that arise in finite and
infinite mixture models, using transportation distances (ie, Wasserstein metrics). The …

We propose a general maximum likelihood empirical Bayes (GMLEB) method for the
estimation of a mean vector based on observations with iid normal errors. We prove that …

Bayesian fractional posteriors Page 1 The Annals of Statistics 2019, Vol. 47, No. 1, 39–66
https://doi.org/10.1214/18-AOS1712 © Institute of Mathematical Statistics, 2019 BAYESIAN …