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A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (30 June 2023) | Viewed by 7329

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Prof. Dr. Elisa Varini

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Institute for Applied Mathematics and Information Technologies “Enrico Magenes” (IMATI), National Research Council (CNR), via Corti 12, 20133 Milano, Italy
Interests: stochastic modelling; Bayesian parametric statistics; statistical seismology

Special Issue Information

Dear Colleagues,

Earth and Environmental Sciences are an increasingly important interdisciplinary area of study in the development of new and effective strategies for mitigation of natural and anthropogenic hazards as well as to support decision-making in an uncertain and complex world. Statisticians are called to face new challenges associated with complex and heterogeneous data, by taking advantage of available statistical and computing techniques as well as by defining appropriate stochastic models, capable of exploiting the physical knowledge on phenomena, for predictions and decisions.

This Special Issue welcomes original papers and critical reviews that contribute new knowledge to help address issues related to Earth and environmental problems at a regional or global scale. In an interdisciplinary context, it covers practical applications of stochastic models and their simulations in the Earth and Environmental Sciences as well as methodological advances in applied and computational statistics.

Prof. Dr. Elisa Varini
Guest Editor

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Keywords

stochastic modelling and statistical methods
applied mathematics
mathematical physics
earth and environmental sciences

Published Papers (5 papers)

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Research

Open AccessArticle

Spatiotemporal Analysis of the Background Seismicity Identified by Different Declustering Methods in Northern Algeria and Its Vicinity

and

Axioms 2023, 12(3), 237; https://doi.org/10.3390/axioms12030237 - 24 Feb 2023

Viewed by 884

Abstract

The main purpose of this paper was to, for the first time, analyse the spatiotemporal features of the background seismicity of Northern Algeria and its vicinity, as identified by different declustering methods (specifically: the Gardner and Knopoff, Gruenthal, Uhrhammer, Reasenberg, Nearest Neighbour, and Stochastic Declustering methods). Each declustering method identifies a different declustered catalogue, namely a different subset of the earthquake catalogue that represents the background seismicity, which is usually expected to be a realisation of a homogeneous Poisson process over time, though not necessarily in space. In this study, a statistical analysis was performed to assess whether the background seismicity identified by each declustering method has the spatiotemporal properties typical of such a Poisson process. The main statistical tools of the analysis were the coefficient of variation, the Allan factor, the Markov-modulated Poisson process (also named switched Poisson process with multiple states), the Morisita index, and the L–function. The results obtained for Northern Algeria showed that, in all cases, temporal correlation and spatial clustering were reduced, but not totally eliminated in the declustered catalogues, especially at long time scales. We found that the Stochastic Declustering and Gruenthal methods were the most successful methods in reducing time correlation. For each declustered catalogue, the switched Poisson process with multiple states outperformed the uniform Poisson model, and it was selected as the best model to describe the background seismicity in time. Moreover, for all declustered catalogues, the spatially inhomogeneous Poisson process did not fit properly the spatial distribution of earthquake epicentres. Hence, the assumption of stationary and homogeneous Poisson process, widely used in seismic hazard assessment, was not met by the investigated catalogue, independently from the adopted declustering method. Accounting for the spatiotemporal features of the background seismicity identified in this study is, therefore, a key element towards effective seismic hazard assessment and earthquake forecasting in Algeria and the surrounding area. Full article

(This article belongs to the Special Issue Stochastic Modelling and Statistical Methods in Earth and Environmental Sciences)

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Open AccessArticle

Temporal Cox Process with Folded Normal Intensity

Orietta Nicolis

Luis M. Riquelme Quezada

and

Germán Ibacache-Pulgar

Axioms 2022, 11(10), 513; https://doi.org/10.3390/axioms11100513 - 28 Sep 2022

Viewed by 992

Abstract

In this work, the case of a Cox Process with Folded Normal Intensity (CP-FNI), in which the intensity is given by

Λ (t) = | Z (t) |

, where

Z (t)

is a stationary Gaussian process, [...] Read more.

In this work, the case of a Cox Process with Folded Normal Intensity (CP-FNI), in which the intensity is given by

Λ (t) = | Z (t) |

, where

Z (t)

is a stationary Gaussian process, is studied. Here, two particular cases are dealt with: (i) when the process

Z (t)

constitutes a family of independent random variables and with a common probability law

N (0, 1)

, and (ii) the case in which

Z (t)

is a second order stationary process, with exponential type covariance function. In these cases, we observe that the properties of the Gaussian process

Z (t)

are naturally transferred to the intensity

Λ (t)

and that very analytical results are achievable from the analytical point of view for the point process

N (t)

. Finally, some simulations are presented in order to appreciate what type of counting phenomena can be modeled by these cases of CP-FNI. In particular, it is interesting to see how the trajectories show a tendency of the events to be grouped in certain periods of time, also leaving long periods of time without the occurrence of events. Full article

(This article belongs to the Special Issue Stochastic Modelling and Statistical Methods in Earth and Environmental Sciences)

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Figure 1

Open AccessArticle

Stochastic Modelling of Red Palm Weevil Using Chemical Injection and Pheromone Traps

Moustafa El-Shahed

Asma Al-Nujiban

and

Nagdy F. Abdel-Baky

Axioms 2022, 11(7), 334; https://doi.org/10.3390/axioms11070334 - 10 Jul 2022

Viewed by 1149

Abstract

This paper deals with the mathematical modelling of the red palm weevil (RPW), Rhynchophorus ferrugineus (Olivier) (Coleoptera: Curculionidae), in date palms using chemical control by utilizing injection and sex pheromone traps. A deterministic and stochastic model for RPW is proposed and analyzed. The existence of a positive global solution for the stochastic RPW model is investigated, and the conditions for the extinction of RPWs from the stochastic system are obtained. The adequate criteria for the presence of a unique ergodic stationary distribution for the RPW system are established by creating suitable Lyapunov functions. The impact of chemical injection and pheromone traps on RPW is demonstrated. The importance of environmental noise on RPW is highlighted and simulated using the Milstein method. Full article

(This article belongs to the Special Issue Stochastic Modelling and Statistical Methods in Earth and Environmental Sciences)

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Figure 1

Open AccessArticle

A Simultaneous Estimation of the Baseline Intensity and Parameters for Modulated Renewal Processes

Jiancang Zhuang

and

Hai-Yen Siew

Axioms 2022, 11(7), 303; https://doi.org/10.3390/axioms11070303 - 23 Jun 2022

Viewed by 935

Abstract

This paper proposes a semiparametric solution to estimate the intensity (hazard) function of modulated renewal processes: a nonparametric estimate for the baseline intensity function together with a parametric estimate of the model parameters of the covariate processes. Based on the martingale property associated with the conditional intensity, we construct a statistic from a residual analysis to estimate the baseline renewal intensity function, when the model parameters of the covariate processes are known. In addition, when the baseline intensity is obtained, the model parameters can be estimated using the usual maximum likelihood estimation. In practice, both the baseline intensity and model parameters are suggested to be estimated simultaneously via an expectation–maximization (E–M)-type iterative algorithm. A more important feature of the newly proposed algorithm is that, given n events in the observation dataset, its computation time is of order

O (n^{2})

, while the Nelson–Aalen–Breslow estimator takes a computation time of order

O (n^{3})

. For illustration, we apply the proposed estimation procedure to a set of data simulated from a modulated gamma renewal process and the aftershock sequence following the

M_{s} 8

Wenchuan earthquake, which occurred in Sichuan Province, China on 12 May 2008. Full article

(This article belongs to the Special Issue Stochastic Modelling and Statistical Methods in Earth and Environmental Sciences)

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Open AccessArticle

An Earthquake-Clustering Model in North Aegean Area (Greece)

Ourania Mangira

Rodolfo Console

Eleftheria Papadimitriou

Maura Murru

and

Vasileios Karakostas

Axioms 2022, 11(6), 249; https://doi.org/10.3390/axioms11060249 - 26 May 2022

Viewed by 1270

Abstract

The investigation of short-term earthquake-clustering features is made feasible through the application of a purely stochastic Epidemic-Type Aftershock Sequence (ETAS) model. The learning period that is used for the estimation of the parameters is composed by earthquakes with M ≥ 2.6 that occurred between January 2008 and May 2017. The model predictability is retrospectively examined for the 12 June 2017 Lesvos earthquake (M_w6.4) and the subsequent events. The construction of time-dependent seismicity maps and comparison between the observed and expected earthquake number are performed in order to temporally and spatially test the evolution of the sequence, respectively. The generation of 127 target events with M ≥ 3.0 in the period June–July 2017, just before the main shock occurrence, is examined in a quantitative evaluation. The statistical criteria used for assessing the model performance are the Relative Operating Characteristic Diagram, the R-score, and the probability gain. Reliable forecasts are provided through the epidemic model testifying its superiority towards a time-invariant Poisson model. Full article

(This article belongs to the Special Issue Stochastic Modelling and Statistical Methods in Earth and Environmental Sciences)

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