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Bayesian statistical models allow us to formalise our knowledge about the world and reason about our uncertainty, but there is a need for better procedures to accurately encode its complexity. One way to do so is through compositional…

In Chib (1995), a method for approximating marginal densities in a Bayesian setting is proposed, with one proeminent application being the estimation of the number of components in a normal mixture. As pointed out in Neal (1999) and…

Uncertainty quantification in reinforcement learning can greatly improve exploration and robustness. Approximate Bayesian approaches have recently been popularized to quantify uncertainty in model-free algorithms. However, so far the focus…

We describe and analyze a broad class of mixture models for real-valued multivariate data in which the probability density of observations within each component of the model is represented as an arbitrary combination of basis functions.…

When two nested models are compared, using a Bayes factor, from an objective standpoint, two seemingly conflicting issues emerge at the time of choosing parameter priors under the two models. On the one hand, for moderate sample sizes, the…

This paper builds on recent research that focuses on regression modeling of continuous bounded data, such as proportions measured on a continuous scale. Specifically, it deals with beta regression models with mixed effects from a Bayesian…

Lack of independence in the residuals from linear regression motivates the use of random effect models in many applied fields. We start from the one-way anova model and extend it to a general class of one-factor Bayesian mixed models,…

Mixture models are a standard tool in statistical analyses, widely used for density modeling and model-based clustering. In this work, we propose a Bayesian mixture model with repulsion between mixture components. Such repulsion helps…

A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric additive models in which the number of additive components may be larger than the sample size, though ideally the true model is believed to include only a small…

We introduce a new empirical Bayes approach for large-scale multiple linear regression. Our approach combines two key ideas: (i) the use of flexible "adaptive shrinkage" priors, which approximate the nonparametric family of scale mixture of…

Scientists continue to develop increasingly complex mechanistic models to reflect their knowledge more realistically. Statistical inference using these models can be challenging since the corresponding likelihood function is often…

In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…

Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…

Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…

We focus on Bayesian inverse problems with Gaussian likelihood, linear forward model, and priors that can be formulated as a Gaussian mixture. Such a mixture is expressed as an integral of Gaussian density functions weighted by a mixing…

Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…

We consider high-dimensional distribution estimation through autoregressive networks. By combining the concepts of sparsity, mixtures and parameter sharing we obtain a simple model which is fast to train and which achieves state-of-the-art…

Variable selection techniques have become increasingly popular amongst statisticians due to an increased number of regression and classification applications involving high-dimensional data where we expect some predictors to be unimportant.…

When observations are organized into groups where commonalties exist amongst them, the dependent random measures can be an ideal choice for modeling. One of the propositions of the dependent random measures is that the atoms of the…

We consider the specification of prior distributions for Bayesian model comparison, focusing on regression-type models. We propose a particular joint specification of the prior distribution across models so that sensitivity of posterior…