Related papers: When are Extreme Events the better predictable, th…

The problem of detecting the presence of a signal that can lead to a disaster is studied. A decision-maker collects data sequentially over time. At some point in time, called the change point, the distribution of data changes. This change…

The big jump principle is a well established mathematical result for sums of independent and identically distributed random variables extracted from a fat tailed distribution. It states that the tail of the distribution of the sum is the…

This paper describes prediction methods for the number of future events from a population of units associated with an on-going time-to-event process. Examples include the prediction of warranty returns and the prediction of the number of…

Risk management is particularly concerned with extreme events, but analysing these events is often hindered by the scarcity of data, especially in a multivariate context. This data scarcity complicates risk management efforts. Various tools…

In this paper, we discuss the emergence of extreme events in a parametrically driven non-polynomial mechanical system with a velocity-dependent potential. We confirm the occurrence of extreme events from the probability distribution…

Uncertainty in return level estimates for rare events, like the intensity of large rainfall events, makes it difficult to develop strategies to mitigate related hazards, like flooding. Latent spatial extremes models reduce uncertainty by…

Finding the most powerful node in a dynamic random network, the largest set in a partition-valued stochastic process, or the largest family in an evolving population at a given time, can be a very difficult problem. This is particularly the…

Practitioners building classifiers often start with a smaller pilot dataset and plan to grow to larger data in the near future. Such projects need a toolkit for extrapolating how much classifier accuracy may improve from a 2x, 10x, or 50x…

We present results for long term and intermediate term prediction algorithms applied to a simple mechanical model of a fault. We use long term prediction methods based, for example, on the distribution of repeat times between large events…

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…

Extreme events, such as rogue waves, earthquakes and stock market crashes, occur spontaneously in many dynamical systems. Because of their usually adverse consequences, quantification, prediction and mitigation of extreme events are highly…

Predicting extreme events in nonlinear dynamical systems is challenging due to a limited understanding of their statistical properties. This study numerically and theoretically investigates the statistical properties of infinite-modal maps…

Conformal prediction is a popular method to construct prediction intervals with marginal coverage guarantees from black-box machine learning models. In applications with potentially high-impact events, such as flooding or financial crises,…

We develop an Euler-type method to predict the evolution of a time-dependent probability measure without explicitly learning an operator that governs its evolution. We use linearized optimal transport theory to prove that the measure-valued…

Likelihood methods for measuring statistical evidence obey the likelihood principle while maintaining bounded and well-controlled frequency properties. These methods lend themselves to sequential study designs because they measure the…

We derive precursors of extreme dissipation events in a turbulent channel flow. Using a recently developed method that combines dynamics and statistics for the underlying attractor, we extract a characteristic state that precedes…

Being able to predict the occurrence of extreme returns is important in financial risk management. Using the distribution of recurrence intervals---the waiting time between consecutive extremes---we show that these extreme returns are…

In public discussions of the quality of forecasts, attention typically focuses on the predictive performance in cases of extreme events. However, the restriction of conventional forecast evaluation methods to subsets of extreme observations…

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…

We introduce and compare computational techniques for sharp extreme event probability estimates in stochastic differential equations with small additive Gaussian noise. In particular, we focus on strategies that are scalable, i.e. their…