We consider the problem of detecting and describing space-time interaction in point process data. We extend existing second-order methods for purely spatial point process data to the spatial-temporal setting. This extension allows us to estimate space-time interaction as a function of spatial and temporal separation, and provides a useful reinterpretation of a popular test, due to Knox, for space-time interaction. Applications to simulated and real data indicate the method's potential.
Get full access to this article
View all access options for this article.
References
1.
Knox G.Detection of low density epidemicity. British Journal of Preventative and Social Medicine1963; 17: 121-27.
2.
Knox G.Epidemology of childhood leukaemia in Northumberland and Durham. British Journal of Preventative and Social Medicine1984; 18: 17-24.
3.
Barton DE, David FNThe random intersection of two graphs. In: David FN ed. Research papers in statistics. New York: Wiley, 1966: 455-590.
4.
Besag J., Diggle PJSimple Monte Carlo tests for spatial pattern. Applied Statistics1977; 26: 327-33.
5.
Williams GWTime-space clustering of disease. In: Cornell RG ed. Statistical methods for cancer studies. New York: Marcel Dekker, 1984:167-227.
6.
Bhopal RS, Diggle PJ, Rowlingson BSPinpointing clusters of apparently sporadic Legionnaires' disease. British Medical Journal1992; 304: 1022-27.
7.
Daley DJ, Vere-Jones D.An introduction to the theory of point processes. New York : Springer-Verlag, 1988.
8.
Stoyan D., Kendall WS, Mecke J.Stochastic geometry and its applications. Berlin: Akademie-Verlag, 1987.
9.
Ripley BDThe second-order analysis of stationary point processes. Journal of Applied Probability1976; 13: 255-66.
10.
Ripley BDModelling spatial patterns (with Discussion). Journal of the Royal Statistical Society, Series B1977; 39: 172-212.
11.
Ripley BDEdge effects in spatial stochastic processes. In: Ranneby B ed. Statistics in theory and practice. Umeå: Swedish University of Agricultural Sciences, 1982: 247-62.
12.
Cliff AD, Ord JKSpatial processes: models and applications. London: Pion, 1981.
13.
Ripley BDSpatial statistics. New York: Wiley .
14.
Diggle PJStatistical analysis of spatial point patterns. London : Academic Press, 1983.
15.
Cressie N.Statistics for spatial data. New York: Wiley, 1991.
16.
Diggle PJA kernel method for smoothing point process data. Applied Statistics1985; 34: 138-47.
17.
Barnard GAContribution to the Discussion of Professor Bartlett's paper. Journal of the Royal Statistical Society, Series B1963; 25: 294.
18.
Gilman EA, Knox EGTemporal-spatial distribution of childhood leukaemias and non-Hodgkin lymphomas in Great Britain. In: Draper G ed. The geographical epidemiology of childhood leukaemia and non-Hodgkin lymphomas in Great Britain, 1966-83. London: HMSO, 1991.
