Point-process models with linearly parametrized intensity for application to earthquake data

1986 ◽  
Vol 23 (A) ◽  
pp. 291-310 ◽  
Author(s):  
Yosihiko Ogata ◽  
Koichi Katsura
Keyword(s):  
Seismic Activity ◽  
Process Models ◽  
Evolutionary Trend ◽  
Conditional Intensity ◽  
Data Set ◽  
Technical Aspects ◽  
Point Process Models ◽  
Earthquake Sequences ◽  
Flexible Models ◽  
Earthquake Data

It is demonstrated that linear parametrization of the conditional intensity provides systematic classes of flexible models which are reasonably useful for calculating maximum likelihoods. To exemplify the modelling, seismic activity around Canberra is decomposed into components of evolutionary trend, clustering and periodicity. The causal relationship between earthquake sequences from two seismic regions is also analysed for a certain Japanese earthquake data set.Some technical aspects of the modelling and calculations are described.

Point-process models with linearly parametrized intensity for application to earthquake data

1986 ◽  
Vol 23 (A) ◽  
pp. 291-310 ◽  
Author(s):  
Yosihiko Ogata ◽  
Koichi Katsura
Keyword(s):  
Seismic Activity ◽  
Process Models ◽  
Evolutionary Trend ◽  
Conditional Intensity ◽  
Data Set ◽  
Technical Aspects ◽  
Point Process Models ◽  
Earthquake Sequences ◽  
Flexible Models ◽  
Earthquake Data

It is demonstrated that linear parametrization of the conditional intensity provides systematic classes of flexible models which are reasonably useful for calculating maximum likelihoods. To exemplify the modelling, seismic activity around Canberra is decomposed into components of evolutionary trend, clustering and periodicity. The causal relationship between earthquake sequences from two seismic regions is also analysed for a certain Japanese earthquake data set. Some technical aspects of the modelling and calculations are described.

A Computationally Efficient Method for Nonparametric Modeling of Neural Spiking Activity with Point Processes

2010 ◽  
Vol 22 (8) ◽  
pp. 2002-2030 ◽  
Author(s):  
Todd P. Coleman ◽  
Sridevi S. Sarma
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Intensity Function ◽  
Process Models ◽  
Conditional Intensity ◽  
Computationally Efficient ◽  
Neural Data ◽  
Neural Spiking ◽  
Point Process Models ◽  
Conditional Intensity Function

Point-process models have been shown to be useful in characterizing neural spiking activity as a function of extrinsic and intrinsic factors. Most point-process models of neural activity are parametric, as they are often efficiently computable. However, if the actual point process does not lie in the assumed parametric class of functions, misleading inferences can arise. Nonparametric methods are attractive due to fewer assumptions, but computation in general grows with the size of the data. We propose a computationally efficient method for nonparametric maximum likelihood estimation when the conditional intensity function, which characterizes the point process in its entirety, is assumed to be a Lipschitz continuous function but otherwise arbitrary. We show that by exploiting much structure, the problem becomes efficiently solvable. We next demonstrate a model selection procedure to estimate the Lipshitz parameter from data, akin to the minimum description length principle and demonstrate consistency of our estimator under appropriate assumptions. Finally, we illustrate the effectiveness of our method with simulated neural spiking data, goldfish retinal ganglion neural data, and activity recorded in CA1 hippocampal neurons from an awake behaving rat. For the simulated data set, our method uncovers a more compact representation of the conditional intensity function when it exists. For the goldfish and rat neural data sets, we show that our nonparametric method gives a superior absolute goodness-of-fit measure used for point processes than the most common parametric and splines-based approaches.

scholarly journals Can the Spatial Point Patterns of Animal Distributions Be Detected Using Sparse Samples? A Case Study of Four Soricomorpha (Mammalia) Species in Poland / Czy Przestrzenny Wzorzec Rozkładu Punktów W Dystrybucji Zwierząt Może Zostać Określony Na Podstawie Rzadkiego Próbkowania? Studium Przypadku Na Czterech Gatunkach Soricomorpha (Mammalia) Występujących W Polsce.

2014 ◽  
Vol 59 (1-4) ◽  
pp. 11-24
Author(s):  
Youhua Chen
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Process Models ◽  
Spatial Point Process ◽  
Data Set ◽  
Point Patterns ◽  
Spatial Point ◽  
Spatial Point Patterns ◽  
Point Process Models ◽  
K Function

Abstract In the present study, Riley's K function and alternative spatial point process models are calculated and compared for the hybrid distributional records of four Soricomorpha species (Talpa europaea, Sorex araneus, Sorex minutus, and Neomys fodiens) in Poland over different sampling sizes. The following spatial point process models are fitted and compared: homogeneous Poisson process (HPP) and inhomogeneous Poisson process (IPP) models. For IPP models, the covariates explaining the trend are latitude and longitude. Spatial process models and true distributional aggregation status (using K function) of the four species are also calculated based on the full observed data set for the purpose to check how many grids are required to sample so as to reflect the true spatial distributional point patterns. When performind tha sampling, the sanpling size 5, 10, 30, 60 and 100 are considered. For each sampling size, 500 replicates are performed to keep consistence and reduce uncertainty. The results showed that, for the full observed data set over the whole territory of Poland, IPP models were much better than the null HPP model for explaining the distribution of Soricomorpha species. For every sample size, the true aggregation status and the associated spatial point process models of each species over the studied area can be perfectly identified when using the information derived from limiting samples only. Based on the results, it is found that around 20% of grid cells should be used as the minimum threshold for accurately detecting the true spatial point patterns

Habitat use of toothed whales in a marine protected area based on point process models

2019 ◽  
Vol 609 ◽  
pp. 239-256 ◽  
Author(s):  
TL Silva ◽  
G Fay ◽  
TA Mooney ◽  
J Robbins ◽  
MT Weinrich ◽  
...  
Keyword(s):  
Habitat Use ◽  
Point Process ◽  
Protected Area ◽  
Marine Protected Area ◽  
Process Models ◽  
Point Process Models

scholarly journals An efficient optimizer for simple point process models

2013 ◽  
Author(s):  
Ahmed Gamal-Eldin ◽  
Guillaume Charpiat ◽  
Xavier Descombes ◽  
Josiane Zerubia
Keyword(s):  
Point Process ◽  
Process Models ◽  
Simple Point ◽  
Point Process Models

A study of the aftershocks and focal mechanism of the Salinas-Watsonville earthquakes of August 31 and September 14, 1963

1965 ◽  
Vol 55 (1) ◽  
pp. 85-106 ◽  
Author(s):  
Agustin Udias
Keyword(s):  
Focal Mechanism ◽  
Seismic Activity ◽  
Main Shock ◽  
San Andreas Fault ◽  
San Andreas ◽  
Principal Axes ◽  
Mobile Stations ◽  
Earthquake Sequences ◽  
Background Seismic Activity

Abstract The earthquake sequences connected with the earthquakes of August 31 and September 14, 1963 in the Salinas-Watsonville region of California are here studied with reference to the background seismic activity. A very favorable distribution of permanent and mobile stations in this area permits the analysis to include earthquakes of small magnitudes. The mechanism of the larger aftershocks of both sequences is found to be similar to the mechanism of the main shock of September 14, 1963. The orientation of the principal axes of stress derived from the focal mechanism of the September 14 earthquake, is related to the strike of the San Andreas fault.

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