Residual analysis for spatial point processes (with discussion)

By Adrian Baddeley, Rolf Turner, Jesper Møller, Martin L. Hazelton. 2005

360 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/a5e8e10b6143382f673ffa607f8003b91b134d89

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In Applied Mathematics

Citations in the corpus

Evaluation of space–time point process models using super‐thinning (2011, methodology): “Although it is true that model fitting will always result in some estimation error, as with standard residual methods such as those described in Baddeley et al. (2005), our proposed methods do not seem to be especially sensitive to one type of model or estimation procedure.”
Second‐order residual analysis of spatiotemporal point processes and applications in model evaluation (2006, methodology): “Baddeley et al. (2005) gave the first-order residuals for a spatial point process X={x1, x2, . . .} based on the Nguyen and Zessin (1979) formula E [ ∑ xi∈X∩D h.xi; X\{xi}/ ] =E [∫ D h.x; X/λP.x; X/µ.dx/ ] , for any measurable set D, where λP is the Papangelou conditional intensity.”
Modern Statistics for Spatial Point Processes * (2007, methodology): “For a Gibbs point process with log Papangelou conditional intensity (24), the first-order potential corresponds to the linear predictor of a generalized linear model (GLM), while the higher order potentials are roughly analogous to the distribution of the errors in a GLM. Recently, Baddeley et al. (”
Autoregressive Mixture Models for Dynamic Spatial Poisson Processes: Application to Tracking Intensity of Violent Crime (2010, background): “There are a variety of different count residual measures for nonhomogeneous Poisson processes, and Baddeley et al. (2005) provide a survey.”
Mixture Modeling for Marked Poisson Processes (2010, background): “Hence, a standard approach to assessing model validity is to compare observed counts to integrated intensity within a set of (possibly overlapping) subregions (e.g., Diggle, 2003; Baddeley et al., 2005).”
Assessment of Point Process Models for Earthquake Forecasting (2013, background): “These types of residuals were described in great detail by Baddeley et al. (2005) and Baddeley, Møller and Pakes (2008).”
Structured Spatio‐Temporal Shot‐Noise Cox Point Process Models, with a View to Modelling Forest Fires (2010, background): “The mean cluster size given by (5) becomes n (y,s) t = λ1(y)λ2(s)δχζ(t − s), and the offspring distribution is simply a bivariate normal distribution with mean y and independent coordinates with variance σ(2).”
Logistic regression for spatial Gibbs point processes (2014, background): “Each component of the vector T1,Wn(X) is a special case of innovations for spatial Gibbs point processes introduced by Baddeley et al. (2005) with variances studied by Baddeley et al. (2008) and asymptotic results225 provided by Coeurjolly & Lavancier (2013) and Coeurjolly & Rubak (2013).”
Bayesian Inference and Model Assessment for Spatial Point Patterns Using Posterior Predictive Samples (2017, methodology): “In particular, for model adequacy, we propose examination of Bayesian residuals (drawing on the work of Baddeley et al., 2005), both realized and predictive, as well as empirical coverage and prior predictive checks through Monte Carlo tests.”