Related papers: Gibbs posterior inference on multivariate quantile…
Bayesian methods estimate a measure of uncertainty by using the posterior distribution. One source of difficulty in these methods is the computation of the normalizing constant. Calculating exact posterior is generally intractable and we…
The martingale posterior framework is a generalization of Bayesian inference where one elicits a sequence of one-step ahead predictive densities instead of the likelihood and prior. Posterior sampling then involves the imputation of unseen…
We study spike-and-slab priors for generalized linear models with possible grouped sparsity. The main result is an oracle Bernstein--von Mises theorem for the fractional posterior under supportwise likelihood assumptions. The proof develops…
We consider discrete nonparametric priors which induce Gibbs-type exchangeable random partitions and investigate their posterior behavior in detail. In particular, we deduce conditional distributions and the corresponding Bayesian…
An important feature of Bayesian statistics is the opportunity to do sequential inference: the posterior distribution obtained after seeing a dataset can be used as prior for a second inference. However, when Monte Carlo sampling methods…
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 priors for several nonparametric Bayesian models which use finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…
Frequentist conditions for asymptotic suitability of Bayesian procedures focus on lower bounds for prior mass in Kullback-Leibler neighbourhoods of the data distribution. The goal of this paper is to investigate the flexibility in criteria…
In this work we consider Bayesian inference problems with intractable likelihood functions. We present a method to compute an approximate of the posterior with a limited number of model simulations. The method features an inverse Gaussian…
In this paper, we study the asymptotic posterior distribution of linear functionals of the density. In particular, we give general conditions to obtain a semiparametric version of the Bernstein-Von Mises theorem. We then apply this general…
We consider a class of non-conjugate priors as a mixing family of distributions for a parameter (e.g., Poisson or gamma rate, inverse scale or precision of an inverse-gamma, inverse variance of a normal distribution) of an exponential…
Bayesian methods provide a natural means for uncertainty quantification, that is, credible sets can be easily obtained from the posterior distribution. But is this uncertainty quantification valid in the sense that the posterior credible…
We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
We derive the Jeffreys prior for the parameter of the Multivariate Ewens Distribution and study some of its properties. In particular, we show that this prior is proper and has no finite moments. We also investigate the impact of this…
Generative Bayesian Filtering (GBF) provides a powerful and flexible framework for performing posterior inference in complex nonlinear and non-Gaussian state-space models. Our approach extends Generative Bayesian Computation (GBC) to…
We propose a robust and scalable framework for variational Bayes (VB) that effectively handles outliers and contamination of arbitrary nature in large datasets. Our approach divides the dataset into disjoint subsets, computes the posterior…
We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's…
Gibbs sampling is a Markov chain Monte Carlo method that is often used for learning and inference on graphical models. Minibatching, in which a small random subset of the graph is used at each iteration, can help make Gibbs sampling scale…
This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. In particular, we improve on current rates of…