In the statistical analysis of spatial point patterns, it is often important to investigate whether the point pattern depends on spatial covariates. This paper describes nonparametric (kernel and local likelihood) methods for estimating the effect of spatial covariates on the point process intensity. Variance estimates and confidence intervals are provided in the case of a Poisson point process. Techniques are demonstrated with simulated examples and with applications to exploration geology and forest ecology.
Ebstein's anomaly is a rare, congenital cardiac anomaly that may result in cyanosis, right heart failure, and tachyarrhythmia during the newborn stage or after adolescence. This study investigated the data of 77 patients diagnosed between 1980 and 2006 at a tertiary care center in Taiwan. Patients were grouped into either an early group or a late group. Survival declined rapidly within the newborn stage in the early group, but declined only during the third decade in the late group. Surgical results were poor (20% success rate) for neonatal systemic-to-pulmonary shunts in those cases with associated pulmonary atresia, but were satisfactory for other surgical modes. Supraventricular tachyarrhythmia occurred in 31 (41%) patients at a median age of 10 years and could be eliminated by radiofrequency ablation (81% success rate), though the recurrence rate was high (41%). In conclusion, other than those cases requiring shunts at the newborn stage, the long-term outcome was favorable.
Abstract. For a spatial point process model fitted to spatial point pattern data, we develop diagnostics for model validation, analogous to the classical measures of leverage and influence in a generalized linear model. The diagnostics can be characterized as derivatives of basic functionals of the model. They can also be derived heuristically (and computed in practice) as the limits of classical diagnostics under increasingly fine discretizations of the spatial domain. We apply the diagnostics to two example datasets where there are concerns about model validity.
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