Johns Hopkins University, Dept. of Biostatistics Working Papers 6-27-2005 Spatio-temporal Point Processes: Methods and Applications Peter J. Diggle Medical Statistics Unit, Lancaster University, UK & Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health,
[email protected] Suggested Citation Diggle, Peter J., "Spatio-temporal Point Processes: Methods and Applications" (June 2005). Johns Hopkins University, Dept. of Biostatistics Working Papers. Working Paper 78. http://biostats.bepress.com/jhubiostat/paper78 This working paper is hosted by The Berkeley Electronic Press (bepress) and may not be commercially reproduced without the permission of the copyright holder. Copyright © 2011 by the authors Spatio-temporal Point Processes: Methods and Applications Peter J Diggle (Department of Mathematics and Statistics, Lancaster University and Department of Biostatistics, Johns Hopkins University School of Public Health) June 27, 2005 1 Introduction This chapter is concerned with the analysis of data whose basic format is (xi; ti) : i = 1; :::; n where each xi denotes the location and ti the corresponding time of occurrence of an event of interest. We shall assume that the data form a complete record of all events which occur within a pre-specified spatial region A and a pre-specified time- interval, (0; T ). We call a data-set of this kind a spatio-temporal point pattern, and the underlying stochastic model for the data a spatio-temporal point process. 1.1 Motivating examples 1.1.1 Amacrine cells in the retina of a rabbit One general approach to analysing spatio-temporal point process data is to extend existing methods for purely spatial data by considering the time of occurrence as a distinguishing feature, or mark, attached to each event.