Related papers: Asymptotically minimax Bayesian predictive densiti…
We propose a Bayesian test of normality for univariate or multivariate data against alternative nonparametric models characterized by Dirichlet process mixture distributions. The alternative models are based on the principles of embedding…
In a remarkable series of papers beginning in 1956, Charles Stein set the stage for the future development of minimax shrinkage estimators of a multivariate normal mean under quadratic loss. More recently, parallel developments have seen…
Within Bayesian nonparametrics, dependent Dirichlet process mixture models provide a highly flexible approach for conducting inference about the conditional density function. However, several formulations of this class make either rather…
We develop Bayesian models for density regression with emphasis on discrete outcomes. The problem of density regression is approached by considering methods for multivariate density estimation of mixed scale variables, and obtaining…
We propose a novel Bayesian model selection technique on linear mixed-effects models to compare multiple treatments with a control. A fully Bayesian approach is implemented to estimate the marginal inclusion probabilities that provide a…
We consider the asymptotic behaviour of the marginal maximum likelihood empirical Bayes posterior distribution in general setting. First we characterize the set where the maximum marginal likelihood estimator is located with high…
We investigate Bayesian shrinkage methods for constructing predictive distributions. We consider the multivariate Normal model with a known covariance matrix and show that the Bayesian predictive density with respect to Stein's harmonic…
We consider the problem of estimating probability density functions based on sample data, using a finite mixture of densities from some component class. To this end, we introduce the $h$-lifted Kullback--Leibler (KL) divergence as a…
Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, however, the algorithm fails to account for any uncertainty in…
Bayesian predictive inference provides a coherent description of entire predictive uncertainty through predictive distributions. We examine several widely used sparsity priors from the predictive (as opposed to estimation) inference…
We present an alternative approach to the Bayesian nonparametric analysis of conditional species richness under two-parameter Poisson Dirichlet priors. We rely on a known characterization by deletion of classes property and on results for…
We consider estimation of the common probability density $f$ of i.i.d. random variables $X_i$ that are observed with an additive i.i.d. noise. We assume that the unknown density $f$ belongs to a class $\mathcal{A}$ of densities whose…
Although continuous density estimation has received abundant attention in the Bayesian nonparametrics literature, there is limited theory on multivariate mixed scale density estimation. In this note, we consider a general framework to…
We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster…
We extend the Bayesian Information Criterion (BIC), an asymptotic approximation for the marginal likelihood, to Bayesian networks with hidden variables. This approximation can be used to select models given large samples of data. The…
The prior distribution on parameters of a sampling distribution is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective which focuses on missing observations as the source of…
The classical mixture of Gaussians model is related to K-means via small-variance asymptotics: as the covariances of the Gaussians tend to zero, the negative log-likelihood of the mixture of Gaussians model approaches the K-means objective,…
We propose information criteria that measure the prediction risk of a predictive density based on the Bayesian marginal likelihood from a frequentist point of view. We derive criteria for selecting variables in linear regression models,…
We consider predictive density estimation under logarithmic score for $d$-dimensional infinitely divisible location models. Taking the formal Bayes predictive density under the Lebesgue prior as a benchmark, we study the Kullback-Leibler…
In causal inference, sensitivity analysis is important to assess the robustness of study conclusions to key assumptions. We perform sensitivity analysis of the assumption that missing outcomes are missing completely at random. We follow a…