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Point processes, temporal
David R. Brillinger, Peter M. Guttorp & Frederic Paik Schoenberg Volume 3, pp 1577–1581
in
Encyclopedia of Environmetrics (ISBN 0471 899976)
Edited by
Abdel H. El-Shaarawi and Walter W. Piegorsch
John Wiley & Sons, Ltd, Chichester, 2002 is an encyclopedic account of the theory of the Point processes, temporal subject.
A temporal point process is a random process whose Examples realizations consist of the times f jg, j 2 , j D 0, š1, š2,... of isolated events scattered in time. A Examples of point processes abound in the point process is also known as a counting process or environment; we have already mentioned times a random scatter. The times may correspond to events of floods. There are also times of earthquakes, of several types. fires, deaths, accidents, hurricanes, storms (hale, Figure 1 presents an example of temporal point ice, thunder), volcanic eruptions, lightning strikes, process data. The figure actually provides three dif- tornadoes, power outages, chemical spills (see ferent ways of representing the timing of floods Meteorological extremes; Natural disasters). on the Amazon River near Manaus, Brazil, dur- ing the period 1892–1992 (see Hydrological ex- tremes)[7]. Questions The formal use of the concept of point process has a long history going back at least to the life tables The questions that scientists ask involving point of Graunt [14]. Physicists contributed many ideas in process data include the following. Is a point pro- the first half of the twentieth century; see, for ex- cess associated with another process? Is the associ- ample, [23]. The book by Daley and Vere-Jones [11] ation between two point processes actually causal? Is there a change or trend in time (see Trend, detecting)? Does the structure change (see Change, 20 detecting)? Are the times clustered? Are the times 15 repelled from each other? What is the predicted behavior? What is the risk (probability) of some 10 event of negative consequence occurring at some 5 future time (see Risk assessment, probabilistic)? How does one learn or describe the relationship of (a) 1900 1920 1940 1960 1980 such processes? How does one carry out system Time (year) identification? 2.0 1.5 Representations 1.0 0.5 A number of methods are used for the representation of point processes and of point process data. The 0.0 figure shows three types of displays. The represen- 1900 1920 1940 1960 1980 (b) Time (year) tations include:
20 ž step function 15 Nt D #f0 <