Multidimensional Residual Analysis of Point Process Models for Earthquake Occurrences

By Frederic Paik Schoenberg. 2003

180 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Graphics and Computer-Aided Design, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/ebd1eadc2045c5f16ad59adf62e732ecd26cd1f1

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In Applied Mathematics

In Computer Graphics and Computer-Aided Design

In Environmental Engineering

Citations in the corpus

A Space–Time Conditional Intensity Model for Evaluating a Wildfire Hazard Index (2005, methodology): “Various methods for constructing a multidimensional residual point process based on random rescaling (Merzbach and Nualart 1986; Nair 1990; Schoenberg 1999) and random thinning (Schoenberg 2003) have been proposed.”
Self-exciting point process models of civilian deaths in Iraq (2011, unknown): “We use variable bandwidth kernel smoothing to construct a smoothed version of the data ( Silverman, 1998 ; Zhuang et al , 2002 ; Schoenberg, 2003 ).”
Consistent Parametric Estimation of the Intensity of a Spatial-temporal Point Process (2005, background): “Key words: maximum likelihood estimation, weighted least squares estimation, consistency, Poisson process, conditional intensity.”
Assessment of Point Process Models for Earthquake Forecasting (2013, methodology): “Thinned residuals are based on the technique of random thinning, which was first introduced by Lewis and Shedler (1979) and Ogata (1981) for the purpose of simulating spatial–temporal point processes and extended for the purpose of model evaluation in Schoenberg (2003).”
Evaluation of space–time point process models using super‐thinning (2011, methodology): “The points that remain are called thinned residual points, and if the estimate O .x; t / D .x; t / almost everywhere, then the residual process, Z, will be homogeneous Poisson with rate b (Schoenberg, 2003).”
Point process diagnostics based on weighted second-order statistics and their asymptotic properties (2009, methodology): “…be a comparison between the various residual second-order statistics proposed here as well as comparison with other methods of residual analysis such as the first-order residuals of Baddeley et al. (2000) or the second-order statistics of the residual processes such as those in Schoenberg (2003).”
Analyzing earthquake clustering features by using stochastic reconstruction (2004, methodology): “To justify the particular models used in this study, we can use likelihood-based model selection procedures and apply the residual analysis [see, e.g., Schoenberg, 2003] to find the overall goodness of fit of the model to the data.”