Related papers: Bayesian approach to extreme-value statistics base…
The conditional maximum-entropy method (abbreviated here as C-MaxEnt) is formulated for selecting prior probability distributions in Bayesian statistics for parameter estimation. This method is inspired by a statistical-mechanical approach…
Statistical extreme value theory is concerned with the use of asymptotically motivated models to describe the extreme values of a process. A number of commonly used models are valid for observed data that exceed some high threshold.…
Maximum entropy (MAXENT) method has a large number of applications in theoretical and applied machine learning, since it provides a convenient non-parametric tool for estimating unknown probabilities. The method is a major contribution of…
The problem of assigning probability distributions which objectively reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of…
In most data-scientific approaches, the principle of Maximum Entropy (MaxEnt) is used to a posteriori justify some parametric model which has been already chosen based on experience, prior knowledge or computational simplicity. In a…
The method of Maximum (relative) Entropy (ME) is used to translate the information contained in the known form of the likelihood into a prior distribution for Bayesian inference. The argument is guided by intuition gained from the…
Data-driven anomaly detection methods typically build a model for the normal behavior of the target system, and score each data instance with respect to this model. A threshold is invariably needed to identify data instances with high (or…
(Jaynes') Method of (Shannon-Kullback's) Relative Entropy Maximization (REM or MaxEnt) can be - at least in the discrete case - according to the Maximum Probability Theorem (MPT) viewed as an asymptotic instance of the Maximum Probability…
A major issue of extreme value analysis is the determination of the shape parameter $\xi$ common to Generalized Extreme Value (GEV) and Generalized Pareto (GP) distributions, which drives the tail behavior, and is of major impact on the…
In classical extreme value theory probabilities of extreme events are estimated assuming all the components of a random vector to be in a domain of attraction of an extreme value distribution. In contrast, the conditional extreme value…
Statistical modeling of multivariate and spatial extreme events has attracted broad attention in various areas of science. Max-stable distributions and processes are the natural class of models for this purpose, and many parametric families…
Predicting extreme events is important in many applications in risk analysis. The extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction.…
The diversity of a community that cannot be fully counted must be inferred. The two preeminent inference methods are the MaxEnt method, which uses information in the form of constraints and Bayes' rule which uses information in the form of…
Statistical inference for extreme values of random events is difficult in practice due to low sample sizes and inaccurate models for the studied rare events. If prior knowledge for extreme values is available, Bayesian statistics can be…
Estimating extreme quantiles is an important task in many applications, including financial risk management and climatology. More important than estimating the quantile itself is to insure zero coverage error, which implies the quantile…
Many economic panel and dynamic models, such as rational behavior and Euler equations, imply that the parameters of interest are identified by conditional moment restrictions. We introduce a novel inference method without any prior…
We prove that information-theoretic maximum entropy (MaxEnt) approach to canonical ensemble is mathematically equivalent to the classic approach of Boltzmann, Gibbs and Darwin-Fowler. The two approaches, however, "interpret" a same…
In this paper an alternative approach to statistical mechanics based on the maximum information entropy principle (MaxEnt) is examined, specifically its close relation with the Gibbs method of ensembles. It is shown that the MaxEnt…
Mixed modeling of extreme values and random effects is relatively unexplored topic. Computational difficulties in using the maximum likelihood method for mixed models and the fact that maximum likelihood method uses available data and does…
Extreme value theory (EVT) is a statistical tool for analysis of extreme events. It has a strong theoretical background, however, we need to choose hyper-parameters to apply EVT. In recent studies of machine learning, techniques of choosing…