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Recently developed survival analysis methods improve upon existing approaches by predicting the probability of event occurrence in each of a number pre-specified (discrete) time intervals. By avoiding placing strong parametric assumptions…

Since long back, scientists have been putting enormous effort to understand earthquake dynamics -the goal is to develop a successful prediction scheme which can provide reliable alarm that an earthquake is imminent. Model studies sometimes…

In the classical stochastic resetting problem, a particle, moving according to some stochastic dynamics, undergoes random interruptions that bring it to a selected domain, and then, the process recommences. Hitherto, the resetting mechanism…

The impact of an extreme climate event depends strongly on its geographical scale. Max-stable processes can be used for the statistical investigation of climate extremes and their spatial dependencies on a continuous area. Most existing…

Self-exciting spatio-temporal point process models predict the rate of events as a function of space, time, and the previous history of events. These models naturally capture triggering and clustering behavior, and have been widely used in…

We compare probabilistic predictions of extreme temperature anomalies issued by two different forecast schemes. One is a dynamical physical weather model, the other a simple data model. We recall the concept of skill scores in order to…

In environmental science applications, extreme events frequently exhibit a complex spatio-temporal structure, which is difficult to describe flexibly and estimate in a computationally efficient way using state-of-art parametric…

Parametric inference for spatial max-stable processes is difficult since the related likelihoods are unavailable. A composite likelihood approach based on the bivariate distribution of block maxima has been recently proposed in the…

Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic…

A likely source of earthquake clustering is static stress transfer between individual events. Previous attempts to quantify the role of static stress for earthquake triggering generally considered only the stress changes caused by large…

When very small particles are suspended in a fluid in motion, they tend to follow the flow. How such tracer particles are mixed, transported, and dispersed by turbulent flow has been successfully described by statistical models. Heavy…

Spatiotemporal correlations of the two-dimensional spring-block (Burridge-Knopoff) model of earthquakes are extensively studied by means of numerical computer simulations. The model is found to exhibit either ``subcritical'' or…

A crucial point in the debate on feasibility of earthquake prediction is the dependence of an earthquake magnitude from past seismicity. Indeed, whilst clustering in time and space is widely accepted, much more questionable is the existence…

Models for extreme values accommodating non-stationarity have been amply studied and evaluated from a parametric perspective. Whilst these models are flexible, in the sense that many parametrizations can be explored, they assume an…

Studying event time series is a powerful approach for analyzing the dynamics of complex dynamical systems in many fields of science. In this paper, we describe the method of event coincidence analysis to provide a framework for quantifying…

Earthquakes rank among the most destructive manifestations of the Earth's dynamics. Can they be predicted? This is often the first question students ask. To answer that right away: no, at present it is not possible to anticipate the date,…

We discuss various statistical distributions of earthquake numbers. Previously we derived several discrete distributions to describe earthquake numbers for the branching model of earthquake occurrence: these distributions are the Poisson,…

The areal modeling of the extremes of a natural process such as rainfall or temperature is important in environmental statistics; for example, understanding extreme areal rainfall is crucial in flood protection. This article reviews recent…

Modelling and forecasting the occurrence of extreme events is especially difficult when the event process is nonstationary, with changes in both the rate at which extremes occur and the magnitude of the extremes when they occur. We approach…

We present theoretical arguments and simulation data indicating that the scaling of earthquake events in models of faults with long-range stress transfer is composed of at least three distinct regions. These regions correspond to three…