Related papers: Bayesian composite confidence interval for the tai…

Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…

Although Bayesian inference is an immensely popular paradigm among a large segment of scientists including statisticians, most applications consider objective priors and need critical investigations (Efron, 2013, Science). While it has…

Bayesian posterior distributions naturally represent parameter uncertainty informed by data. However, when the parameter space is complex, as in many nonparametric settings where it is infinite-dimensional or combinatorially large, standard…

On the basis of Nelson-Aalen product-limit estimator of a randomly censored distribution function, we introduce a kernel estimator to the tail index of right-censored Pareto-like data. Under some regularity assumptions, the consistency and…

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…

Compared to mean regression and quantile regression, the literature on modal regression is very sparse. A unifying framework for Bayesian modal regression is proposed, based on a family of unimodal distributions indexed by the mode, along…

We propose an analytical approach to the computation of tail probabilities of compound distributions whose individual components have heavy tails. Our approach is based on the contour integration method, and gives rise to a representation…

We revisit and generalize the concept of composite likelihood as a method to make a probabilistic inference by aggregation of multiple Bayesian agents, thereby defining a class of predictive models which we call composite Bayesian. This…

The construction of the Bayesian credible (confidence) interval for a Poisson observable including both the signal and background with and without systematic uncertainties is presented. Introducing the conditional probability satisfying the…

We consider heavy-tailed distributions and compare the well-known estimators of the tail index, based on extreme value theory with a comparatively recent estimator based on a different idea.

The non-asymptotic tail bounds of random variables play crucial roles in probability, statistics, and machine learning. Despite much success in developing upper bounds on tail probability in literature, the lower bounds on tail…

Bayesian clustering methods have the widely touted advantage of providing a probabilistic characterization of uncertainty in clustering through the posterior distribution. An amazing variety of priors and likelihoods have been proposed for…

The paper presents an efficient method for simulating the tails of a target variable Z=h(X) which depends on a set of basic variables X=(X_1, ..., X_n). To this aim, variables X_i, i=1, ..., n are sequentially simulated in such a manner…

Modern statistical analyses often encounter datasets with massive sizes and heavy-tailed distributions. For datasets with massive sizes, traditional estimation methods can hardly be used to estimate the extreme value index directly. To…

We develop an efficient simulation algorithm for computing the tail probabilities of the infinite series $S = \sum_{n \geq 1} a_n X_n$ when random variables $X_n$ are heavy-tailed. As $S$ is the sum of infinitely many random variables, any…

Bayesian model comparison is often based on the posterior distribution over the set of compared models. This distribution is often observed to concentrate on a single model even when other measures of model fit or forecasting ability…

We study objective Bayesian inference for linear regression models with residual errors distributed according to the class of two-piece scale mixtures of normal distributions. These models allow for capturing departures from the usual…

We propose Bayesian Conformal Prediction (BCP), a framework that combines Bayesian posterior predictive distributions with PAC-style conformal risk control to produce prediction sets with finite-sample coverage guarantees. Standard…

The block maxima method is one of the most popular approaches for extreme value analysis with independent and identically distributed observations in the domain of attraction of an extreme value distribution. The lack of a rigorous study on…

It was shown that when one disposes of a parametric information of the truncation distribution, the semiparametric estimator of the distribution function for truncated data (Wang, 1989) is more efficient than the nonparametric one. On the…