Related papers: On Posterior Consistency of Tail Index for Bayesia…
We consider nonparametric estimation of a mixed discrete-continuous distribution under anisotropic smoothness conditions and possibly increasing number of support points for the discrete part of the distribution. For these settings, we…
The martingale posterior framework is a generalization of Bayesian inference where one elicits a sequence of one-step ahead predictive densities instead of the likelihood and prior. Posterior sampling then involves the imputation of unseen…
In this paper, we propose a novel frequency-severity joint trip-level risk index that combines the frequency of abnormal driving patterns with a severity component reflecting how extreme such behavior is relative to a portfolio-level…
When model uncertainty is handled by Bayesian model averaging (BMA) or Bayesian model selection (BMS), the posterior distribution possesses a desirable "oracle property" for parametric inference, if for large enough data it is nearly as…
Dirichlet process mixture models (DPMM) play a central role in Bayesian nonparametrics, with applications throughout statistics and machine learning. DPMMs are generally used in clustering problems where the number of clusters is not known…
In this paper, we propose an estimator of the second-order parameter of randomly right-truncated Pareto-type distributions data and establish its consistency and asymptotic normality. Moreover, we derive an asymptotically unbiased estimator…
We show that the full-sample bootstrap is asymptotically valid for constructing confidence intervals for high-quantiles, tail probabilities, and other tail parameters of a univariate distribution. This resolves the doubts that have been…
We propose a Bayesian copula-based framework to quantify clinically interpretable joint tail risks from paired continuous biomarkers. After converting each biomarker margin to rank-based pseudo-observations, we model dependence using…
Learning-based solutions for long-tailed recognition face difficulties in generalizing on balanced test datasets. Due to imbalanced data prior, the learned \textit{a posteriori} distribution is biased toward the most frequent (head)…
In this paper non-asymptotic exponential estimates are derived for the tail distribution of polynomial martingale differences in terms unconditional tails distributions of summands. Applications are considered in the theory of polynomials…
Finite mixture models are a useful statistical model class for clustering and density approximation. In the Bayesian framework finite mixture models require the specification of suitable priors in addition to the data model. These priors…
Various natural phenomena exhibit spatial extremal dependence at short spatial distances. However, existing models proposed in the spatial extremes literature often assume that extremal dependence persists across the entire domain. This is…
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…
Many econometric models can be analyzed as finite mixtures. We focus on two-component mixtures and we show that they are nonparametrically point identified by a combination of an exclusion restriction and tail restrictions. Our…
In the real world, the frequency of occurrence of objects is naturally skewed forming long-tail class distributions, which results in poor performance on the statistically rare classes. A promising solution is to mine tail-class examples to…
This paper investigates the consistency of a posterior distribution in the single-measurement fractional Calder\'on problem with additive Gaussian noise. We consider a Bayesian framework with rescaled and Gaussian sieve priors, using a…
Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid…
We propose a Bayesian approach using improper priors for hierarchical linear mixed models with flexible random effects and residual error distributions. The error distribution is modelled using scale mixtures of normals, which can capture…
The purpose of this paper is to show that the use of heavy-tailed distributions in Financial problems is theoretically baseless and can lead to significant misunderstandings. The reason for this the authors see in an incorrect…
Heavy-tailed distributions are widely used in robust mixture modelling due to possessing thick tails. As a computationally tractable subclass of the stable distributions, sub-Gaussian $\alpha$-stable distribution received much interest in…