Time series pattern discovery is of great importance in a large variety of environmental and engineering applications, from supporting predictive models to helping to understand hidden underlying processes. This work develops a multiresolution time series method for extracting patterns in weather records, particular temperature data. The topic is important, as, given a warming climate, morbidit...

Statistics of central tendency and dispersion may not capture relevant or desired characteristics of the distribution of continuous phenomena and, thus, they may not adequately describe temporal patterns of change. Here, we present two methodological approaches that can help to identify temporal changes in environmental regimes. First, we use higher-order statistical moments (skewness and kurto...

In extreme events such as the Egyptian 2011 uprising, the online social media technology enables many people from heterogeneous backgrounds to join the event in response to the crisis. This form of collectivity (online crowd) is usually formed spontaneously with minimum constraints in the relationships among the members. The theories of collective behavior suggest that the pattern of behavior i...

37 We discuss behavioral studies directed at understanding how probability 38 information is represented in motor and economic tasks. By formulating the behavioral 39 tasks in the language of statistical decision theory, we can compare performance in 40 equivalent tasks in different domains. Subjects in traditional economic decision-making 41 tasks often misrepresent the probability of rare eve...

• In many areas of application, a typical requirement is to estimate a high quantile χ1−p of probability 1−p, a value, high enough, so that the chance of an exceedance of that value is equal to p, small. The semi-parametric estimation of high quantiles depends not only on the estimation of the tail index γ, the primary parameter of extreme events, but also on an adequate estimation of a scale f...

This is about a personal journey starting from my lifelong skepticism about statistical significance tests — perhaps the most mis-applied of all mathematical theories, especially as regards extreme events — toward a new clarity and power in the use of probability theory and a clear resolution of old dilemmas about subjectivity versus objectivity. There is little original thought here. Rather, t...

The residual dependence index of bivariate Gaussian distributions is determined by the correlation coefficient. This tail index is of certain statistical importance when extremes and related rare events of bivariate samples with asymptotic independent components are being modeled. In this paper we calculate the partial residual dependence indices of a multivariate elliptical random vector assum...

Roughly speaking, Large Deviations is a theory of rare events. It is probably the most active field in probability theory at present, one which has many surprising ramifications. One of its applications is to the analysis of the tails of probability distributions and, in recent years, this aspect of the theory has been widely used in queuing theory. The aim of this tutorial is to introduce the ...

In this paper, we extract and validate high-frequency oscillations in the port of Ploče, based on sea level data from one year (March 2002-March 2003) measured at a tide gauge in the harbor. Frequency was analyzed by applying stationary (spectral) and non-stationary (wavelet and filtering) analyses of the data to extract temporal characteristics of the fundamental seiches with a period of 30 mi...

Using the tail index of returns on US equities as a summary measure of extreme behaviour, we examine changes in the equity markets surrounding the development of program trading for portfolio insurance, the crash of 1987, and the subsequent introduction of circuit breakers and other changes in market architecture. Recentlydeveloped tests for the null of constancy of the tail index, versus the a...