Related papers: Default Bayesian Analysis for the Multivariate Ewe…
The Jeffreys divergence is a renown symmetrization of the oriented Kullback-Leibler divergence broadly used in information sciences. Since the Jeffreys divergence between Gaussian mixture models is not available in closed-form, various…
Variance parameters in additive models are typically assigned independent priors that do not account for model structure. We present a new framework for prior selection based on a hierarchical decomposition of the total variance along a…
We consider a decision maker who is unaware of objects to be sampled and thus cannot form beliefs about the occurrence of particular objects. Ex ante she can form beliefs about the occurrence of novelty and the frequencies of yet to be…
Jeffrey's rule has been generalized by Wagner to the case in which new evidence bounds the possible revisions of a prior probability below by a Dempsterian lower probability. Classical probability kinematics arises within this…
Finite mixture and Markov-switching models generalize and, therefore, nest specifications featuring only one component. While specifying priors in the two: the general (mixture) model and its special (single-component) case, it may be…
This article introduces a new method for eliciting prior distributions from experts. The method models an expert decision-making process to infer a prior probability distribution for a rare event $A$. More specifically, assuming there…
Gibbs type priors have been shown to be natural generalizations of Dirichlet process (DP) priors used for intricate applications of Bayesian nonparametric methods. This includes applications to mixture models and to species sampling models…
Reference priors are theoretically attractive for the analysis of geostatistical data since they enable automatic Bayesian analysis and have desirable Bayesian and frequentist properties. But their use is hindered by computational hurdles…
This paper argues that the half-Cauchy distribution should replace the inverse-Gamma distribution as a default prior for a top-level scale parameter in Bayesian hierarchical models, at least for cases where a proper prior is necessary. Our…
This paper aims at developing a quasi-Bayesian analysis of the nonparametric instrumental variables model, with a focus on the asymptotic properties of quasi-posterior distributions. In this paper, instead of assuming a distributional…
We study the rate of Bayesian consistency for hierarchical priors consisting of prior weights on a model index set and a prior on a density model for each choice of model index. Ghosal, Lember and Van der Vaart [2] have obtained general…
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 present an elementary non-recursive formula for the multivariate moments of the Dirichlet distribution on the standard simplex, in terms of the pattern inventory of the moments' exponents. We obtain analog formulas for the multivariate…
We propose a two-component mixture of a noninformative (diffuse) and an informative prior distribution, weighted through the data in such a way to prefer the first component if a prior-data conflict arises. The data-driven approach for…
We exploit a suitable moment-based characterization of the mixture of Poisson distribution for developing Bayesian inference for the unknown size of a finite population whose units are subject to multiple occurrences during an enumeration…
One-step ahead prediction for the multinomial model is considered. The performance of a predictive density is evaluated by the average Kullback-Leibler divergence from the true density to the predictive density. Asymptotic approximations of…
The recent literature on deep learning offers new tools to learn a rich probability distribution over high dimensional data such as images or sounds. In this work we investigate the possibility of learning the prior distribution over neural…
The behavior of many Bayesian models used in machine learning critically depends on the choice of prior distributions, controlled by some hyperparameters that are typically selected by Bayesian optimization or cross-validation. This…
In practical situations, most experimental designs often yield unbalanced data which have different numbers of observations per unit because of cost constraints, or missing data, etc. In this paper, we consider the Bayesian approach to…
We propose a measure of the impact of any two choices of prior distributions by quantifying the Wasserstein distance between the respective resulting posterior distributions at any fixed sample size. We illustrate this measure on the…