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Replication of scientific studies is important for assessing the credibility of their results. However, there is no consensus on how to quantify the extent to which a replication study replicates an original result. We propose a novel…
The ability to backpropagate stochastic gradients through continuous latent distributions has been crucial to the emergence of variational autoencoders and stochastic gradient variational Bayes. The key ingredient is an unbiased and…
One of the well-known challenges in optimal experimental design is how to efficiently estimate the nested integrations of the expected information gain. The Gaussian approximation and associated importance sampling have been shown to be…
Bayesian variable selection requires sampling from a posterior distribution that combines discrete model indicators with continuously varying parameters, a challenge often addressed through reversible jump Markov chain Monte Carlo (RJMCMC).…
Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…
We study location-scale mixture priors for nonparametric statistical problems, including multivariate regression, density estimation and classification. We show that a rate-adaptive procedure can be obtained if the prior is properly…
Bayesian analyses combine information represented by different terms in a joint Bayesian model. When one or more of the terms is misspecified, it can be helpful to restrict the use of information from suspect model components to modify…
Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…
For predictive modeling relying on Bayesian inversion, fully independent, or ``mean-field'', Gaussian distributions are often used as approximate probability density functions in variational inference since the number of variational…
Benchmarking estimation and its risk evaluation is a practically important issue in small area estimation. While Bayesian methods have been widely adopted in small area estimation, existing benchmarking approaches are often ad-hoc, such as…
We propose a method for estimating the posterior distribution of a standard geostatistical model. After choosing the model formulation and specifying a prior, we use normal mixture densities to approximate the posterior distribution. The…
We study posterior contraction behaviors for parameters of interest in the context of Bayesian mixture modeling, where the number of mixing components is unknown while the model itself may or may not be correctly specified. Two…
Multidimensional data is often associated with uncertainties that are not well-described by normal distributions. In this work, we describe how such distributions can be projected to a low-dimensional space using uncertainty-aware principal…
We introduce a prior for the parameters of univariate continuous distributions, based on the Wasserstein information matrix, which is invariant under reparameterisations. We discuss the links between the proposed prior with information…
We study frequentist risk properties of predictive density estimators for mean mixtures of multivariate normal distributions, involving an unknown location parameter $\theta \in \mathbb{R}^d$, and which include multivariate skew normal…
The study of almost surely discrete random probability measures is an active line of research in Bayesian nonparametrics. The idea of assuming interaction across the atoms of the random probability measure has recently spurred significant…
Gaussian mixtures are a powerful and widely used tool to model non-Gaussian estimation problems. They are able to describe measurement errors that follow arbitrary distributions and can represent ambiguity in assignment tasks like point set…
Bayesian learning in undirected graphical models|computing posterior distributions over parameters and predictive quantities is exceptionally difficult. We conjecture that for general undirected models, there are no tractable MCMC (Markov…
The normal-normal hierarchical model (NNHM) constitutes a simple and widely used framework for meta-analysis. In the common case of only few studies contributing to the meta-analysis, standard approaches to inference tend to perform poorly,…
We consider the problem of approximating a general Gaussian location mixture by finite mixtures. The minimum order of finite mixtures that achieve a prescribed accuracy (measured by various $f$-divergences) is determined within constant…