Related papers: Statistical Prediction of Peaks Over a Threshold
Given a nonlinear model, a probabilistic forecast may be obtained by Monte Carlo simulations. At a given forecast horizon, Monte Carlo simulations yield sets of discrete forecasts, which can be converted to density forecasts. The resulting…
The heavy-tailed behavior of the generalized extreme-value distribution makes it a popular choice for modeling extreme events such as floods, droughts, heatwaves, wildfires, etc. However, estimating the distribution's parameters using…
This paper deals with optimally-robust parameter estimation in generalized Pareto distributions (GPDs). These arise naturally in many situations where one is interested in the behavior of extreme events as motivated by the…
Max-stable processes are the most popular models for high-impact spatial extreme events, as they arise as the only possible limits of spatially-indexed block maxima. However, likelihood inference for such models suffers severely from the…
An empirical Bayes problem has an unknown prior to be estimated from data. The predictive recursion (PR) algorithm provides fast nonparametric estimation of mixing distributions and is ideally suited for empirical Bayes applications. This…
One of the main goal of extreme value analysis is to estimate the probability of rare events given a sample from an unknown distribution. The upper tail behavior of this distribution is described by the extreme value index. We present a new…
The extreme value index is a fundamental parameter in univariate Extreme Value Theory (EVT). It captures the tail behavior of a distribution and is central in the extrapolation beyond observed data. Among other semi-parametric methods (such…
Metrics of model goodness-of-fit, model comparison, and model parameter estimation are the main categories of statistical problems in science. Bayesian and frequentist methods that address these questions often rely on a likelihood…
Extreme values of real phenomena are events that occur with low frequency, but can have a large impact on real life. These are, in many practical problems, high-dimensional by nature (e.g. Tawn, 1990; Coles and Tawn, 1991). To study these…
Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…
Random variables of the generalized Pareto distribution, can be transformed to that of the Pareto distribution. Explicit expressions exist for the maximum likelihood estimators of the parameters of the Pareto distribution. The performance…
Rare weather and climate events, such as heat waves and floods, can bring tremendous social costs. Climate data is often limited in duration and spatial coverage, and climate forecasting has often turned to simulations of climate models to…
Randomness in scientific estimation is generally assumed to arise from unmeasured or uncontrolled factors. However, when combining subjective probability estimates, heterogeneity stemming from people's cognitive or information diversity is…
We review some recent developments which make use of the concept of `superstatistics', an effective description for nonequilibrium systems with a varying intensive parameter such as the inverse temperature. We describe how the asymptotic…
Threshold selection is a critical issue for extreme value analysis with threshold-based approaches. Under suitable conditions, exceedances over a high threshold have been shown to follow the generalized Pareto distribution (GPD)…
The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated…
Aiming to estimate extreme precipitation forecast quantiles, we propose a nonparametric regression model that features a constant extreme value index. Using local linear quantile regression and an extrapolation technique from extreme value…
This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are…
Bayesian methods provide a natural means for uncertainty quantification, that is, credible sets can be easily obtained from the posterior distribution. But is this uncertainty quantification valid in the sense that the posterior credible…
We investigate Bayesian predictive inference for finite population quantities when there are unequal probabilities of selection. Only limited information about the sample design is available; i.e., only the first-order selection…