Related papers: Comparing Spike and Slab Priors for Bayesian Varia…

Many inference problems involve inferring the number $N$ of components in some region, along with their properties $\{\mathbf{x}_i\}_{i=1}^N$, from a dataset $\mathcal{D}$. A common statistical example is finite mixture modelling. In the…

In this work, we propose a Bayesian type sparse deep learning algorithm. The algorithm utilizes a set of spike-and-slab priors for the parameters in the deep neural network. The hierarchical Bayesian mixture will be trained using an…

Nonparametric varying coefficient (NVC) models are useful for modeling time-varying effects on responses that are measured repeatedly for the same subjects. When the number of covariates is moderate or large, it is desirable to perform…

Bayesian profile regression mixture models (BPRM) allow to assess a health risk in a multi-exposed population. These mixture models cluster individuals according to their exposure profile and their health risk. However, their results, based…

In multivariate spline regression, the number and locations of knots influence the performance and interpretability significantly. However, due to non-differentiability and varying dimensions, there is no desirable frequentist method to…

We study Bayesian linear regression models with skew-symmetric scale mixtures of normal error distributions. These kinds of models can be used to capture departures from the usual assumption of normality of the errors in terms of heavy…

Finite mixture model is an important branch of clustering methods and can be applied on data sets with mixed types of variables. However, challenges exist in its applications. First, it typically relies on the EM algorithm which could be…

In this work, we address the problem of solving a series of underdetermined linear inverse problems subject to a sparsity constraint. We generalize the spike-and-slab prior distribution to encode a priori correlation of the support of the…

In Bayesian statistics, the marginal likelihood, also known as the evidence, is used to evaluate model fit as it quantifies the joint probability of the data under the prior. In contrast, non-Bayesian models are typically compared using…

Frequentist robust variable selection has been extensively investigated in high-dimensional regression. Despite success, developing the corresponding statistical inference procedures remains a challenging task. Recently, tackling this…

Bayes linear analysis and approximate Bayesian computation (ABC) are techniques commonly used in the Bayesian analysis of complex models. In this article we connect these ideas by demonstrating that regression-adjustment ABC algorithms…

A method for implicit variable selection in mixture of experts frameworks is proposed. We introduce a prior structure where information is taken from a set of independent covariates. Robust class membership predictors are identified using a…

Markov Chain Monte Carlo (MCMC) sampling is computationally expensive, especially for complex models. Alternative methods make simplifying assumptions about the posterior to reduce computational burden, but their impact on predictive…

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…

Integrative analyses based on statistically relevant associations between genomics and a wealth of intermediary phenotypes (such as imaging) provide vital insights into their clinical relevance in terms of the disease mechanisms. Estimates…

We propose a posterior for Bayesian Likelihood-Free Inference (LFI) based on generalized Bayesian inference. To define the posterior, we use Scoring Rules (SRs), which evaluate probabilistic models given an observation. In LFI, we can…

Screening traditionally refers to the problem of detecting active inputs in the computer model. In this paper, we develop methodology that applies to screening, but the main focus is on detecting active inputs not in the computer model…

Commonly used priors for Vector Autoregressions (VARs) induce shrinkage on the autoregressive coefficients. Introducing shrinkage on the error covariance matrix is sometimes done but, in the vast majority of cases, without considering the…

We propose a novel Bayesian wavelet regression approach using a three-component spike-and-slab prior for wavelet coefficients, combining a point mass at zero, a moment (MOM) prior, and an inverse moment (IMOM) prior. This flexible prior…

Sparse Bayesian factor models are routinely implemented for parsimonious dependence modeling and dimensionality reduction in high-dimensional applications. We provide theoretical understanding of such Bayesian procedures in terms of…