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Probabilistic models with flexible tail behavior have important applications in engineering and earth science. We introduce a nonlinear normalizing transformation and its inverse based on the deformed lognormal and exponential functions proposed by Kaniadakis. The deformed exponential transform can be used to generate skewed data from normal variates. We apply this transform to a censored autoregressive model for the generation of precipitation time series. We also highlight the connection between the heavy-tailed κ -Weibull distribution and weakest-link scaling theory, which makes the κ -Weibull suitable for modeling the mechanical strength distribution of materials. Finally, we introduce the κ -lognormal probability distribution and calculate the generalized (power) mean of κ -lognormal variables. The κ -lognormal distribution is a suitable candidate for the permeability of random porous media. In summary, the κ -deformations allow for the modification of tails of classical distribution models (e.g., Weibull, lognormal), thus enabling new directions of research in the analysis of spatiotemporal data with skewed distributions. [ABSTRACT FROM AUTHOR]

We present different data analytic methodologies that have been applied in order to understand the evolution of the first wave of the Coronavirus disease 2019 in the Republic of Cyprus and the effect of different intervention measures that have been taken by the government. Change point detection has been used in order to estimate the number and locations of changes in the behaviour of the collected data. Count time series methods have been employed to provide short term projections and a number of various compartmental models have been fitted to the data providing with long term projections on the pandemic's evolution and allowing for the estimation of the effective reproduction number. [ABSTRACT FROM AUTHOR]

Spatially distributed processes can be modeled as random fields. The complex spatial dependence is then incorporated in the joint probability density function. Knowledge of the joint probability density allows predicting missing data. While environmental data often exhibit significant deviations from Gaussian behavior (rainfall, wind speed, and earthquakes being characteristic examples), only a few non-Gaussian joint probability density functions admit explicit expressions. In addition, random field models are computationally costly for big datasets. We propose an "effective distribution" approach which is based on the product of univariate conditional probability density functions modified by local interactions. The effective densities involve local parameters that are estimated by means of kernel regression. The prediction of missing data is based on the median value from an ensemble of simulated states generated from the effective distribution model. The latter can capture non-Gaussian dependence and is applicable to large spatial datasets, since it does not require the storage and inversion of large covariance matrices. We compare the predictive performance of the effective distribution approach with classical geostatistical methods using Gaussian and non-Gaussian synthetic data. We also apply the effective distribution approach to the reconstruction of gaps in large raster data. [ABSTRACT FROM AUTHOR]

Predicting rare events, such as high level up-crossings, for spatio-temporal processes plays an important role in the analysis of the occurrence and impact of potential catastrophes in, for example, environmental settings. Designing a system which predicts these events with high probability, but with few false alarms, is clearly desirable. In this paper an optimal alarm system in space over time is introduced and studied in detail. These results generalize those obtained by de Maré (Ann. Probab. 8, 841-850, 1980) and Lindgren (Ann. Probab. 8, 775-792, 1980, Ann. Probab. 13, 804-824, 1985) for stationary stochastic processes evolving in continuous time and are applied here to stationary Gaussian random fields. [ABSTRACT FROM AUTHOR]

Wind power is a renewable energy resource, that has relatively cheap installation costs and it is highly possible that will become the main energy resource in the near future. Wind power needs to be integrated efficiently into electricity grids, and to optimize the power dispatch, techniques to predict the level of wind power and the associated variability are critical. Ideally, one would like to obtain reliable probability density forecasts for the wind power distributions. We aim at contributing to the literature of wind power prediction by developing and analysing a spatio-temporal methodology for wind power production, that is tested on wind power data from Denmark. We use anisotropic spatio-temporal correlation models to account for the propagation of weather fronts, and a transformed latent Gaussian field model to accommodate the probability masses that occur in wind power distribution due to chains of zeros. We apply the model to generate multi-step ahead probability predictions for wind power generated at both locations where wind farms already exist but also to nearby locations. [ABSTRACT FROM AUTHOR]

We study the distribution of phases and amplitudes for the spectral representation of weighted moving averages of a general noise measure. The simple independent structure, known for the Gaussian case, and involving Rayleigh amplitude and uniform phase distributions, is lost for the non Gaussian noise case. We show that the amplitude/phase distributions exhibit a rich and more complex structure depending not just on the covariance of the process but specifically on the form of the kernel and the noise distribution. We present a theoretical tool for studying these distributions that follows from a proof of the spectral theorem that yields an explicit expression for the spectral measure. The main interest is in noise measures based on second-order Lévy motions since such measures are easily available through independent sampling. We approximate the spectral stochastic measure by independent noise increments which allows us to obtain amplitude/phase distributions that is of fundamental interest for analyzing processes in the frequency domain. For the purpose of approximating the moving average process through sums of trigonometric functions, we assess the mean square error of discretization of the spectral representation. For a specified accuracy, the approximation is explicitly given. We illustrate the method for the moving averages driven by the Laplace motion. [ABSTRACT FROM AUTHOR]

A daily stochastic spatiotemporal precipitation generator that yields precipitation realizations that are quantitatively consistent is described. The methodology relies on a latent Gaussian field that drives both the occurrence and intensity of the precipitation process. For the precipitation intensity, the marginal distributions, which are space and time dependent, are described by a composite model of a gamma distribution for observations below some threshold with a generalized Pareto distribution modeling the excesses above the threshold. Model parameters are estimated from data and extrapolated to locations and times with no direct observations using linear regression of position covariates. One advantage of such a model is that stochastic generator parameters are readily available at any location and time of the year inside the stationarity regions. The methodology is illustrated for a network of 12 locations in Sweden. Performance of the model is judged through its ability to accurately reproduce a series of spatial dependence measures and weather indices. [ABSTRACT FROM AUTHOR]

ABSTRACT We tackle an important although rarely addressed question of accounting for a variety of asymmetries frequently observed in stochastic temporal/spatial records. First, we review some measures intending to capture such asymmetries that have been introduced on various occasions in the past and then propose a family of measures that is motivated by Rice's formula for crossing level distributions of the slope. We utilize those asymmetry measures to demonstrate how a class of second-order models built on the skewed Laplace distributions can account for sample path asymmetries. It is shown that these models are capable of mimicking not only distributional skewness but also more complex geometrical asymmetries in the sample path such as tilting, front-back slope asymmetry and time irreversibility. Simple moment-based estimation techniques are briefly discussed to allow direct application to modelling and fitting actual records. [ABSTRACT FROM AUTHOR]

We discuss general non-stationary spatio-temporal surfaces that involve dynamics governed by velocity fields. The approach formalizes and expands previously used models in analysis of satellite data of significant wave heights. We start with homogeneous spatial fields. By applying an extension of the standard moving average construction we obtain models which are stationary in time. The resulting surface changes with time but is dynamically inactive since its velocities, when sampled across the field, have distributions centered at zero. We introduce a dynamical evolution to such a field by composing it with a dynamical flow governed by a given velocity field. This leads to non-stationary models. The models are extensions of the earlier discretized autoregressive models which account for a local velocity of traveling surface. We demonstrate that for such a surface its dynamics is a combination of dynamics introduced by the flow and the dynamics resulting from the covariance structure of the underlying stochastic field. We extend this approach to fields that are only locally stationary and have their parameters varying over a larger spatio-temporal horizon. [ABSTRACT FROM AUTHOR]

The surface of the ocean, and so such quantities as the significant wave height, , can be thought of as a random surface that develops over time. In this paper, we explore certain types of random fields in space and time, with and without dynamics that may or may not be driven by a physical law, as models for the significant wave height. Reanalysis data is used to estimate the sea-state motion which is modeled as a hidden Markov chain in a state space framework by means of an AR(1) process or in the presence of the dispersion relation. Parametric covariance models with and without dynamics are fitted to reanalysis and satellite data and compared to the empirical covariance functions. The derived models have been validated against satellite and buoy data. Copyright © 2010 JohnWiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The Lamperti transformation of a self-similar process is a stationary process. In particular, the fractional Brownian motion transforms to the second order stationary Gaussian process. This process is represented as a series of independent processes. The terms of this series are Ornstein-Uhlenbeck processes if H < 1/2, and linear combinations of two dependent Ornstein-Uhlenbeck processes whose two dimensional structure is Markovian if H > 1/2. From the representation effective approximations of the process are derived. The corresponding results for the fractional Brownian motion are obtained by applying the inverse Lamperti transformation. Implications for simulating the fractional Brownian motion are discussed. [ABSTRACT FROM AUTHOR]