Related papers: Correlations between rare events due to long-term …

The complexity of human interactions with social and natural phenomena is mirrored in the way we describe our experiences through natural language. In order to retain and convey such a high dimensional information, the statistical…

Temporal correlations in the time series observed in various systems have been characterized by the autocorrelation function. Such correlations can be explained by heavy-tailed interevent time distributions as well as by correlations…

Avalanches are often defined as signals higher than some detection level in bursty systems. The choice of the detection threshold affects the number of avalanches, but it can also affect their temporal correlations. We simulated the…

We consider the extreme value statistics of correlated random variables that arise from a Langevin equation. Recently, it was shown that the extreme values of the Ornstein-Uhlenbeck process follow a different distribution than those…

Estimating the probability of rare channel conditions is a central challenge in ultra-reliable wireless communication, where random events, such as deep fades, can cause sudden variations in the channel quality. This paper proposes a…

The probability of rare and extreme events is an important quantity for design purposes. However, computing the probability of rare events can be expensive because only a few events, if any, can be observed. To this end, it is necessary to…

Individual-specific, time-constant, random effects are often used to model dependence and/or to account for omitted covariates in regression models for longitudinal responses. Longitudinal studies have known a huge and widespread use in the…

Alternating recurrent events, where subjects experience two potentially correlated event types over time, are common in healthcare, social, and behavioral studies. Often there is a primary event of interest that, when triggered, initiates a…

In many complex systems, large events are believed to follow power-law, scale-free probability distributions, so that the extreme, catastrophic events are unpredictable. Here, we study coupled chaotic oscillators that display extreme…

A discrete-time random process is described which can generate bursty sequences of events. A Bernoulli process, where the probability of an event occurring at time $t$ is given by a fixed probability $x$, is modified to include a memory…

Inhomogeneous temporal processes, like those appearing in human communications, neuron spike trains, and seismic signals, consist of high-activity bursty intervals alternating with long low-activity periods. In recent studies such bursty…

It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but…

We propose autoregressive Bayesian semi-parametric models for waiting times between recurrent events. The aim is two-fold: inference on the effect of possibly time-varying covariates on the gap times and clustering of individuals based on…

This paper shows that one cannot learn the probability of rare events without imposing further structural assumptions. The event of interest is that of obtaining an outcome outside the coverage of an i.i.d. sample from a discrete…

Energy markets and the associated energy futures markets play a crucial role in global economies. We investigate the statistical properties of the recurrence intervals of daily volatility time series of four NYMEX energy futures, which are…

This paper studies binary logistic regression for rare events data, or imbalanced data, where the number of events (observations in one class, often called cases) is significantly smaller than the number of nonevents (observations in the…

Extreme events can come either from point processes, when the size or energy of the events is above a certain threshold, or from time series, when the intensity of a signal surpasses a threshold value. We are particularly concerned by the…

We analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations) in the presence of an absorbing boundary. An analytically solvable model is presented, in which a dynamical phase-transition occurs…

Mass violence, almost no matter how defined, is (thankfully) rare. Rare events are very difficult to study in a systematic manner. Standard statistical procedures can fail badly and usefully accurate forecasts of rare events often are…

Recently developed information communication technologies, particularly the Internet, have affected how we, both as individuals and as a society, create, store, and recall information. Internet also provides us with a great opportunity to…