Estimation and Inference for Self-exciting Point Processes with Applications to Social Networks and Earthquake Seismology
Estimation and Inference for Self-exciting Point Processes with Applications to Social Networks and Earthquake Seismology

Author: Eric Warren Fox

Publisher:

Published: 2015

Total Pages: 100

ISBN-13:

DOWNLOAD EBOOK

Self-exciting point processes describe random sequences of events where the occurrence of an event increases the likelihood that subsequent events occur nearby in time and space. Models for self-exciting point processes have many important applications to diverse topics such as earthquake and crime forecasting, epidemiology, invasive species, and social networks. The first part of this dissertation discusses a new application of self-exciting point processes to modeling the times when e-mails are sent by individuals in a social network. The proposed models are fit to datasets from West Point Military Academy and the Enron Corporation, and the resulting parameter estimates characterize communication behaviors and leadership roles for users in each network. We argue that the self-exciting models adequately capture major temporal clustering features in the data and perform better than traditional stationary Poisson models. The second part of this dissertation discusses the nonparametric method of Marsan and Lengline (2008) for estimating space-time Hawkes point process models of earthquake occurrences. Their method provides an estimate of a stationary background rate for mainshocks, and a histogram estimate of the triggering function for the rate of aftershocks following an earthquake. At each step of the procedure the model estimates rely on computing the probability each earthquake is a mainshock or aftershock of a previous event. We focus on improving Marsan and Lengline's method by proposing novel ways to incorporate a non-stationary background rate, and adding error bars to the histogram estimates which capture the sampling variability and bias in the estimation of the underlying seismic process. A simulation study is designed to validate and assess new methodology. An application to earthquake data from the Tohoku District in Japan is also discussed, and the results are compared to a well established parametric model of seismicity for this region.

Earthquake Occurrence
Earthquake Occurrence

Author: Rodolfo Console

Publisher: John Wiley & Sons

Published: 2017-08-07

Total Pages: 166

ISBN-13: 1786301245

DOWNLOAD EBOOK

Earthquake Occurrence provides the reader with a review of algorithms applicable for modeling seismicity, such as short-term earthquake clustering and pseudo-periodic long-term behavior of major earthquakes. The concept of the likelihood ratio of a set of observations under different hypotheses is applied for comparison among various models. In short-term models, known by the term ETAS, the occurrence space and time rate density of earthquakes is modeled as the sum of two terms, one representing the independent or spontaneous events, and the other representing the activity triggered by previous earthquakes. Examples of the application of such algorithms in real cases are also reported. Dealing with long-term recurrence models, renewal time-dependent models, implying a pseudo-periodicity of earthquake occurrence, are compared with the simple time-independent Poisson model, in which every event occurs regardless of what has occurred in the past. The book also introduces a number of computer codes developed by the authors over decades of seismological research.

Estimation of Spatial-Temporal Hawkes Models for Earthquake Occurrences
Estimation of Spatial-Temporal Hawkes Models for Earthquake Occurrences

Author: James Molyneux

Publisher:

Published: 2018

Total Pages: 92

ISBN-13:

DOWNLOAD EBOOK

Point processes have long been used as an effective modeling technique in the forecasting of earthquakes. In this dissertation, we evaluate the ability of earthquake focal mechanisms to predict the locational direction of future events and the usefulness of more complicated point process models including such covariates. We also introduce a new computational method for estimating parameters of point processes models using the Stoyan-Grabarnik estimator which avoids the need to numerically compute the intractable integral term needed to compute estimates via maximum likelihood.

Some Methods of Assessing and Estimating Point Processes Models for Earthquake Occurrences
Some Methods of Assessing and Estimating Point Processes Models for Earthquake Occurrences

Author: Alejandro Veen

Publisher:

Published: 2006

Total Pages: 166

ISBN-13: 9780542901522

DOWNLOAD EBOOK

The third part of this work applies the weighted K-function to assess the goodnessof-fit of a class of point process models for the spatial distribution of earthquakes in Southern California. Then, the proposed EM-type algorithm is used to estimate declustered background seismicity rates of geologically distinct regions in Southern California.

Statistical Methods and Modeling of Seismogenesis
Statistical Methods and Modeling of Seismogenesis

Author: Nikolaos Limnios

Publisher: John Wiley & Sons

Published: 2021-03-31

Total Pages: 336

ISBN-13: 1119825032

DOWNLOAD EBOOK

The study of earthquakes is a multidisciplinary field, an amalgam of geodynamics, mathematics, engineering and more. The overriding commonality between them all is the presence of natural randomness. Stochastic studies (probability, stochastic processes and statistics) can be of different types, for example, the black box approach (one state), the white box approach (multi-state), the simulation of different aspects, and so on. This book has the advantage of bringing together a group of international authors, known for their earthquake-specific approaches, to cover a wide array of these myriad aspects. A variety of topics are presented, including statistical nonparametric and parametric methods, a multi-state system approach, earthquake simulators, post-seismic activity models, time series Markov models with regression, scaling properties and multifractal approaches, selfcorrecting models, the linked stress release model, Markovian arrival models, Poisson-based detection techniques, change point detection techniques on seismicity models, and, finally, semi-Markov models for earthquake forecasting.

Statistical Seismology
Statistical Seismology

Author: David Vere-Jones

Publisher: Pageoph Topical Volumes

Published: 2005-07-19

Total Pages: 382

ISBN-13:

DOWNLOAD EBOOK

Statistical Seismology aims to bridge the gap between physics-based and statistics-based models. This volume provides a combination of reviews, methodological studies, and applications, which point to promising efforts in this field. The volume will be useful to students and professional researchers alike, who are interested in using stochastic modeling for probing the nature of earthquake phenomena, as well as an essential ingredient for earthquake forecasting.

Modelling Critical and Catastrophic Phenomena in Geoscience
Modelling Critical and Catastrophic Phenomena in Geoscience

Author: Pratip Bhattacharyya

Publisher: Springer

Published: 2006-09-10

Total Pages: 530

ISBN-13: 3540353755

DOWNLOAD EBOOK

This book presents a broad survey of models for critical and catastrophic phenomena in the geosciences, with strong emphasis on earthquakes. It assumes the perspective of statistical physics, which provides the theoretical frame for dealing with complex systems in general. This volume addresses graduate students wishing to specialize in the field and researchers working or interested in the field having a background in the physics, geosciences or applied mathematics.