Related papers: Comparison Between Bayesian and Frequentist Tail P…

We derive upper bounds on the tail conditional expectation of binomial and Poisson random variables. Those upper bounds are subsequently employed to the problem of obtaining non-asymptotic lower bounds on the probability that the…

We prove an exponential probability tail inequality for positive semidefinite quadratic forms in a subgaussian random vector. The bound is analogous to one that holds when the vector has independent Gaussian entries.

In this paper we compare and contrast the behavior of the posterior predictive distribution to the risk of the maximum a posteriori estimator for the random features regression model in the overparameterized regime. We will focus on the…

We study a new estimator for the tail index of a distribution in the Frechet domain of attraction that arises naturally by computing subsample maxima. This estimator is equivalent to taking a U-statistic over a Hill estimator with two order…

The problem of testing mutually exclusive hypotheses with dependent test statistics is considered. Bayesian and frequentist approaches to multiplicity control are studied and compared to help gain understanding as to the effect of test…

Different questions related with analysis of extreme values and outliers arise frequently in practice. To exclude extremal observations and outliers is not a good decision because they contain important information about the observed…

Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…

In this paper, we introduce reduced-bias estimators for the estimation of the tail index of a Pareto-type distribution. This is achieved through the use of a regularised weighted least squares with an exponential regression model for…

In this paper we consider a stochastic model of perpetuity-type. In contrast to the classical affine perpetuity model of Kesten [12] and Goldie [8] all discount factors in the model are mutually independent. We prove that the tails of the…

Frequentist (classical) and the Bayesian approaches to the construction of confidence limits are compared. Various examples which illustrate specific problems are presented. The Likelihood Principle and the Stopping Rule Paradox are…

Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the…

Despite their importance in supporting experimental conclusions, standard statistical tests are often inadequate for research areas, like the life sciences, where the typical sample size is small and the test assumptions difficult to…

In this paper, we derive tail approximations of integrals of exponential functions of Gaussian random fields with varying mean functions and approximations of the associated point processes. This study is motivated naturally by multiple…

Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…

An examination is made of the differing implications from applying the two mainstream interpretations of probability, frequentist and Bayesian, to QM (quantum mechanics) theory for the Bohm-EPR experiment. The joint probability distribution…

Jeffreys-Lindley paradox is a case where frequentist and Bayesian hypothesis testing methodologies contradict with each other. This has caused confusion among data analysts for selecting a methodology for their statistical inference tasks.…

Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as…

We marshall the arguments for preferring Bayesian hypothesis testing and confidence sets to frequentist ones. We define admissible solutions to inference problems, noting that Bayesian solutions are admissible. We give seven weaker…

We suggest a simple Gaussian mixture model for data generation that complies with Feldman's long tail theory (2020). We demonstrate that a linear classifier cannot decrease the generalization error below a certain level in the proposed…

Chebyshev's inequality provides an upper bound on the tail probability of a random variable based on its mean and variance. While tight, the inequality has been criticized for only being attained by pathological distributions that abuse the…