Geometrically Corrected Second Order Analysis of Events on a Linear Network, with Applications to Ecology and Criminology
MetadataShow full item record
We study point patterns of events that occur on a network of lines, such as road accidents recorded on a road network. Okabe and Yamada developed a 'network K function', analogous to Ripley's K function, for analysis of such data. However, values of the network K-function depend on the network geometry, making interpretation difficult. In this study we propose a correction of the network K-function that intrinsically compensates for the network geometry. This geometrical correction restores many natural and desirable properties of K, including its direct relationship to the pair correlation function. For a completely random point pattern, on any network, the corrected network K-function is the identity. The corrected estimator is intrinsically corrected for edge effects and has approximately constant variance. We obtain exact and asymptotic expressions for the bias and variance of under complete randomness. We extend these results to an 'inhomogeneous' network K-function which compensates for a spatially varying intensity of points. We demonstrate applications to ecology (webs of the urban wall spider Oecobius navus) and criminology (street crime in Chicago). © 2011 Board of the Foundation of the Scandinavian Journal of Statistics.
Showing items related by title, author, creator and subject.
Arora, Balwinder Singh (2012)The precise positioning applications have long been carried out using dual frequency carrier phase and code observables from the Global Positioning System (GPS). The carrier phase observables are very precise in comparison ...
Van Der Werf, Steven Martĳn (2010)In recent years, a great deal of attention has been given to wireless connectivity solutions that are capable of establishing wireless ad-hoc networks between mobile nodes. Whilst most of these networks are formed using ...
PPREMO: A prospective cohort study of preterm infant brain structure and function to predict neurodevelopmental outcomeGeorge, J.; Boyd, Roslyn; Colditz, P.; Rose, S.; Pannek, K.; Fripp, J.; Lingwood, B.; Lai, M.; Kong, A.; Ware, R.; Coulthard, A.; Finn, C.; Bandaranayake, S. (2015)© 2015 George et al. Background: More than 50 percent of all infants born very preterm will experience significant motor and cognitive impairment. Provision of early intervention is dependent upon accurate, early ...