Related papers: Modelling Skewed and Heavy-Tailed Errors in Bayesi…

Asymptotic theory of tail index estimation has been studied extensively in the frequentist literature on extreme values, but rarely in the Bayesian context. We investigate whether popular Bayesian kernel mixture models are able to support…

Heavy tails are often found in practice, and yet they are an Achilles heel of a variety of mainstream random probability measures such as the Dirichlet process (DP). The first contribution of this paper focuses on characterizing the tails…

Across the empirical sciences, few statistical procedures rival the popularity of the frequentist t-test. In contrast, the Bayesian versions of the t-test have languished in obscurity. In recent years, however, the theoretical and practical…

Diffusion models achieve state-of-the-art generation quality across many applications, but their ability to capture rare or extreme events in heavy-tailed distributions remains unclear. In this work, we show that traditional diffusion and…

Multivariate distributions that allow for asymmetry and heavy tails are important building blocks in many econometric and statistical models. The Unified Skew-t (UST) is a promising choice because it is both scalable and allows for a high…

Considered here are robust subgroup-classifier learning and testing in change-plane regressions with heavy-tailed errors, which can identify subgroups as a basis for making optimal recommendations for individualized treatment. A new…

In this paper, we introduce a novel model for the meta-analysis of proportions that integrates the standard random-effects model (REM) with an extreme value theory (EVT)-based component. The proposed model, named XT-REM (Extreme-Tail Random…

We formalise and generalise the definition of the family of univariate double two--piece distributions, obtained by using a density--based transformation of unimodal symmetric continuous distributions with a shape parameter. The resulting…

In this study, we propose a robust mixture regression procedure based on the skew t distribution to model heavy-tailed and/or skewed errors in a mixture regression setting. Using the scale mixture representation of the skew t distribution,…

This article tackles the old problem of prediction via a nonparametric transformation model (NTM) in a new Bayesian way. Estimation of NTMs is known challenging due to model unidentifiability though appealing because of its robust…

Forecast combination methods have traditionally emphasized symmetric loss functions, particularly squared error loss, with equally weighted combinations often justified as a robust approach under such criteria. However, these justifications…

We investigate the existence and severity of local modes in posterior distributions from Bayesian analyses. These are known to occur in posterior tails resulting from heavy-tailed error models such as those used in robust regression. To…

In the framework of censored data modeling, the classical linear regression model that assumes normally distributed random errors has received increasing attention in recent years, mainly for mathematical and computational convenience.…

Recurrent binary outcomes within individuals, such as hospital readmissions, often reflect latent risk processes that evolve over time. Conventional methods like generalized linear mixed models and generalized estimating equations estimate…

Many generalised distributions exist for modelling data with vastly diverse characteristics. However, very few of these generalisations of the normal distribution have shape parameters with clear roles that determine, for instance, skewness…

We comment on the recent paper by Azzalini et al. (2015) on two different distributions proposed in the literature for the modelling of data that have asymmetric and possibly long-tailed clusters. They are referred to as the restricted and…

Existing Bayesian models, especially nonparametric Bayesian methods, rely on specially conceived priors to incorporate domain knowledge for discovering improved latent representations. While priors can affect posterior distributions through…

In this work, we study the convergence \emph{in high probability} of clipped gradient methods when the noise distribution has heavy tails, ie., with bounded $p$th moments, for some $1<p\le2$. Prior works in this setting follow the same…

Models of biological systems often have many unknown parameters that must be determined in order for model behavior to match experimental observations. Commonly-used methods for parameter estimation that return point estimates of the…

In recent decades, statisticians have been increasingly encountering spatial data that exhibit non-Gaussian behaviors such as asymmetry and heavy-tailedness. As a result, the assumptions of symmetry and fixed tail weight in Gaussian…