Estimation of the components of an ETAS (Epidemic Type Aftershock Sequence) model for earthquake description.
Non-parametric background seismicity can be estimated through FLP (Forward Likelihood Predictive), while parametric components are estimated through maximum likelihood.
The two estimation steps are alternated until convergence is obtained.
For each event the probability of being a background event is estimated and used as a weight for declustering steps. Many options to control the estimation process are present, together with some diagnostic tools. Some descriptive functions for earthquakes catalogs are present; also
profile methods are defined for main output (objects of class
|Depends:||R (>= 2.14.0), mapdata,rgl|
etasclass is the main function of the package
The package is intended for the estimation of the ETAS model for seismicity description (introduced by Ogata (1988), see reference), but theoretically it can be used for other fields of application.
Marcello Chiodi and Giada Adelfio
Maintainer: Marcello Chiodi<[email protected]>
Adelfio G, Chiodi M (2009). Second-Order Diagnostics for Space-Time Point Processes with Application to Seismic Events. Environmetrics, 20(8), 895-911. doi:10.1002/env.961.
Adelfio, G. and Chiodi, M. (2013) Mixed estimation technique in semi-parametric space-time point processes for earthquake description. Proceedings of the 28th International Workshop on Statistical Modelling 8-13 July, 2013, Palermo (Muggeo VMR, Capursi V, Boscaino G, Lovison G, editors). Vol. 1. pp.65-70.
Adelfio, G. and Chiodi, M. (2015) Alternated estimation in semi-parametric space-time branching-type point processes with application to seismic catalogs. Stochastic Environmental Research and Risk Assessment 29(2), pp. 443-450. DOI: 10.1007/s00477-014-0873-8
Adelfio G, Chiodi M (2015). FLP Estimation of Semi-Parametric Models for Space-Time Point Processes and Diagnostic Tools. Spatial Statistics, 14(B), 119-132. doi:10.1016/j.spasta.2015.06.004.
Adelfio G, Schoenberg FP (2009). Point Process Diagnostics Based on Weighted Second- Order Statistics and Their Asymptotic Properties. The Annals of the Institute of Statistical Mathematics, 61(4), 929-948. doi:10.1007/s10463-008-0177-1.
Chiodi, M. and Adelfio, G., (2011) Forward Likelihood-based predictive approach for space-time processes. Environmetrics, vol. 22 (6), pp. 749-757. DOI:10.1002/env.1121.
Chiodi, M. and Adelfio, G., (2017) Mixed Non-Parametric and Parametric Estimation Techniques in R Package etasFLP for Earthquakes' Description. Journal of Statistical Software, vol. 76 (3), pp. 1-28. DOI: 10.18637/jss.v076.i03
Console, R., Jackson, D. D. and Kagan, Y. Y. Using the ETAS model for Catalog Declustering and Seismic Background Assessment. Pure Applied Geophysics 167, 819–830 (2010). DOI:10.1007/s00024-010-0065-5.
Nicolis, O., Chiodi, M. and Adelfio G. (2015) Windowed ETAS models with application to the Chilean seismic catalogs, Spatial Statistics, Volume 14, Part B, November 2015, Pages 151-165, ISSN 2211-6753, http://dx.doi.org/10.1016/j.spasta.2015.05.006.
Ogata, Y. Statistical models for earthquake occurrences and residual analysis for point processes. Journal of the American Statistical Association, 83, 9–27 (1988).
Veen, A. and Schoenberg, F.P. Estimation of space-time branching process models in seismology using an EM-type algorithm. Journal of the American Statistical Association, 103(482), 614–624 (2008).
Zhuang, J., Ogata, Y. and Vere-Jones, D. Stochastic declustering of space-time earthquake occurrences. Journal of the American Statistical Association, 97, 369–379 (2002). DOI:10.1198/016214502760046925.
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