Related papers: Model misspecification in peaks over threshold ana…
Data of the form of event times arise in various applications. A simple model for such data is a non-homogeneous Poisson process (NHPP) which is specified by a rate function that depends on time. We consider the problem of having access to…
Modelling excesses over a high threshold using the Pareto or generalized Pareto distribution (PD/GPD) is the most popular approach in extreme value statistics. This method typically requires high thresholds in order for the (G)PD to fit…
The a posteriori error estimates are studied for a class of nonlinear stead-state Poisson-Nernst-Planck equations, which are a coupled system consisting of the Nernst-Planck equation and the Poisson equation. Both the global upper bounds…
The occurrence of successive extreme observations can have an impact on society. In extreme value theory there are parameters to evaluate the effect of clustering of high values, such as the extremal index. The estimation of the extremal…
We use a functional analogue of the quantile function for probability measures on $\mathbb{R}^d$ to characterize a novel limit Poisson point process for radially recentred and rescaled random vectors under a radial-directional…
Finite Gaussian mixture models are widely used for model-based clustering of continuous data. Nevertheless, since the number of model parameters scales quadratically with the number of variables, these models can be easily…
In recent years, advances in high throughput sequencing technology have led to a need for specialized methods for the analysis of digital gene expression data. While gene expression data measured on a microarray take on continuous values…
We propose a general modeling framework for marked Poisson processes observed over time or space. The modeling approach exploits the connection of the nonhomogeneous Poisson process intensity with a density function. Nonparametric Dirichlet…
Motivated by examples from extreme value theory we introduce the general notion of a cluster process as a limiting point process of returns of a certain event in a time series. We explore general invariance properties of cluster processes…
We investigate statistical inference across time scales. We take as toy model the estimation of the intensity of a discretely observed compound Poisson process with symmetric Bernoulli jumps. We have data at different time scales:…
To obtain reliable results of expertise, which usually use individual and group expert pairwise comparisons, it is important to summarize (aggregate) expert estimates provided that they are sufficiently consistent. There are several ways to…
We propose an empirical Bayes estimator based on Dirichlet process mixture model for estimating the sparse normalized mean difference, which could be directly applied to the high dimensional linear classification. In theory, we build a…
The tail chain of a Markov chain can be used to model the dependence between extreme observations. For a positive recurrent Markov chain, the tail chain aids in describing the limit of a sequence of point processes $\{N_n,n\geq1\}$,…
In many contexts such as queuing theory, spatial statistics, geostatistics and meteorology, data are observed at irregular spatial positions. One model of this situation involves considering the observation points as generated by a Poisson…
In this paper, we deal with the problem of calibrating thresholding rules in the setting of Poisson intensity estimation. By using sharp concentration inequalities, oracle inequalities are derived and we establish the optimality of our…
A well-known stochastic model for intermittent fluctuations in physical systems is investigated. The model is given by a super-position of uncorrelated exponential pulses, and the degree of pulse overlap is interpreted as an intermittency…
Using an intrinsic approach, we study some properties of random fields which appear as tail fields of regularly varying stationary random fields. The index set is allowed to be a general locally compact Hausdorff Abelian group $\mathbb{G}$.…
Designs conditions for marine structures are typically informed by threshold-based extreme value analyses of oceanographic variables, in which excesses of a high threshold are modelled by a generalized Pareto (GP) distribution. Too low a…
The statistical modeling of discrete extremes has received less attention than their continuous counterparts in the Extreme Value Theory (EVT) literature. One approach to the transition from continuous to discrete extremes is the modeling…
We present local ensembles, a method for detecting underspecification -- when many possible predictors are consistent with the training data and model class -- at test time in a pre-trained model. Our method uses local second-order…