Related papers: Tail Sensitivity Analysis in Bayesian Networks

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…

In high-dimensions, the prior tails can have a significant effect on both posterior computation and asymptotic concentration rates. To achieve optimal rates while keeping the posterior computations relatively simple, an empirical Bayes…

Despite the successes of probabilistic models based on passing noise through neural networks, recent work has identified that such methods often fail to capture tail behavior accurately, unless the tails of the base distribution are…

We prove tail estimates for variables $\sum_i f(X_i)$, where $(X_i)_i$ is the trajectory of a random walk on an undirected graph (or, equivalently, a reversible Markov chain). The estimates are in terms of the maximum of the function $f$,…

To ensure that real-world infrastructure is safe and durable, systems are designed to not fail for any but the most rarely occurring parameter values. By only happening deep in the tails of the parameter distribution, failure probabilities…

We investigate a way of comparing and classifying tails of random variables. Our approach extends the notion of classical indices, such as exponential and moment indices, which are widely used measuring heaviness of tail functions. A…

Many complex networks in natural and social phenomena have often been characterized by heavy-tailed degree distributions. However, due to rapidly growing size of network data and concerns on privacy issues about using these data, it becomes…

The estimation of loss distributions for dynamic portfolios requires the simulation of scenarios representing realistic joint dynamics of their components. We propose a novel data-driven approach for simulating realistic, high-dimensional…

We study the empirical version of halfspace depths with the objective of establishing a connection between the rates of convergence and the tail behaviour of the corresponding underlying distributions. The intricate interplay between the…

We consider a model for multivariate data with heavy-tailed marginal distributions and a Gaussian dependence structure. The different marginals in the model are allowed to have non-identical tail behavior in contrast to most popular…

Heavy tailed distributions present a tough setting for inference. They are also common in industrial applications, particularly with Internet transaction datasets, and machine learners often analyze such data without considering the biases…

Bias reduction in tail estimation has received considerable interest in extreme value analysis. Estimation methods that minimize the bias while keeping the mean squared error (MSE) under control, are especially useful when applying…

Assessing dependence within co-movements of financial instruments has been of much interest in risk management. Typically, indices of tail dependence are used to quantify the strength of such dependence, although many of the indices…

We consider situations in Bayesian analysis where we have a family of priors $\nu_h$ on the parameter $\theta$, where $h$ varies continuously over a space $\mathcal{H}$, and we deal with two related problems. The first involves sensitivity…

We explore the use of higher-order tail area approximations for Bayesian simulation. These approximations give rise to an alternative simulation scheme to MCMC for Bayesian computation of marginal posterior distributions for a scalar…

The relationship between a response variable and its covariates can vary significantly, especially in scenarios where covariates take on extremely high or low values. This paper introduces a max-linear tail regression model specifically…

Robust Bayesian methods for high-dimensional regression problems under diverse sparse regimes are studied. Traditional shrinkage priors are primarily designed to detect a handful of signals from tens of thousands of predictors in the…

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…

A novel statistical method is proposed and investigated for estimating a heavy tailed density under mild smoothness assumptions. Statistical analyses of heavy-tailed distributions are susceptible to the problem of sparse information in the…

We propose a Bayesian variable selection method in the framework of modal regression for heavy-tailed responses. An efficient expectation-maximization algorithm is employed to expedite parameter estimation. A test statistic is constructed…