Related papers: A weakly informative default prior distribution fo…

We provide a framework for assessing the default nature of a prior distribution using the property of regular variation, which we study for global-local shrinkage priors. In particular, we demonstrate the horseshoe priors, originally…

This is a follow-up paper of Polson and Scott (2012, Bayesian Analysis), which claimed that the half-Cauchy prior is a sensible default prior for a scale parameter in hierarchical models. For estimation of a p-variate normal mean under the…

We introduce a novel class of Bayesian mixtures for normal linear regression models which incorporates a further Gaussian random component for the distribution of the predictor variables. The proposed cluster-weighted model aims to…

We explore the estimation of generalized additive models using basis expansion in conjunction with Bayesian model selection. Although Bayesian model selection is useful for regression splines, it has traditionally been applied mainly to…

We propose a novel Bayesian nonparametric classification model that combines a Gaussian process prior for the latent function with a Dirichlet process prior for the link function, extending the interpretative framework of de Finetti…

This paper develops a methodology for approximating the posterior first two moments of the posterior distribution in Bayesian inference. Partially specified probability models, which are defined only by specifying means and variances, are…

For dimension reduction in $l_1$, the method of {\em Cauchy random projections} multiplies the original data matrix $\mathbf{A} \in\mathbb{R}^{n\times D}$ with a random matrix $\mathbf{R} \in \mathbb{R}^{D\times k}$ ($k\ll\min(n,D)$) whose…

We consider a new learning model in which a joint distribution over vector pairs $(x,y)$ is determined by an unknown function $c(x)$ that maps input vectors $x$ not to individual outputs, but to entire {\em distributions\/} over output…

We propose a class of structured diffusion models, in which the prior distribution is chosen as a mixture of Gaussians, rather than a standard Gaussian distribution. The specific mixed Gaussian distribution, as prior, can be chosen to…

We develop a fully Bayesian, logistic tracking algorithm with the purpose of providing classification results that are unbiased when applied uniformly to individuals with differing sensitive variable values. Here, we consider bias in the…

The nonparametric regression model with normal errors has been extensively studied, both from the frequentist and Bayesian viewpoint. A central result in Bayesian nonparametrics is that under assumptions on the prior, the data-generating…

Distributionally balanced sampling designs are low-discrepancy probability designs obtained by minimizing the expected discrepancy between the auxiliary-variable distribution of a random sample and the target population distribution.…

Biased sampling designs can be highly efficient when studying rare (binary) or low variability (continuous) endpoints. We consider longitudinal data settings in which the probability of being sampled depends on a repeatedly measured…

The predictive quality of machine learning models is typically measured in terms of their (approximate) expected prediction accuracy or the so-called Area Under the Curve (AUC). Minimizing the reciprocals of these measures are the goals of…

Bayesian hierarchical models are commonly employed for inference in count datasets, as they account for multiple levels of variation by incorporating prior distributions for parameters at different levels. Examples include Beta-Binomial,…

We offer a general Bayes theoretic framework to derive posterior contraction rates under a hierarchical prior design: the first-step prior serves to assess the model selection uncertainty, and the second-step prior quantifies the prior…

Zero-shot learning methods typically assume that the new, unseen classes encountered during deployment come from the same distribution as the the classes in the training set. However, real-world scenarios often involve class distribution…

Generalized linear models are a popular tool in applied statistics, with their maximum likelihood estimators enjoying asymptotic Gaussianity and efficiency. As all models are wrong, it is desirable to understand these estimators' behaviours…

This paper considers a Bayesian approach for inclusion detection in nonlinear inverse problems using two known and popular push-forward prior distributions: the star-shaped and level set prior distributions. We analyze the convergence of…

Standard nonlinear regression is commonly used when modeling indifference points due to its ability to closely follow observed data, resulting in a good model fit. However, standard nonlinear regression currently lacks a reasonable…