Scoring probability forecasts for point processes: The entropy score and information gain

Journal of Applied Probability

Volumn 41A, Issue , 2004, Pages 297-312

  Daley, Daryl J ^a   Vere Jones, David ^b  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b VICTORIA UNIVERSITY OF WELLINGTON   (New Zealand)

Author keywords

Entropy score; Information gain; Probability gain

Indexed keywords

EID: 20344372973     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1082552206     Document Type: Article

References (24)

1. Abramowitz, M. and Stegun, I. A. (eds) (1992). Handbook of Mathematical Functions. Dover, NewYork. (Ninth Dover printing of 10th Government Printing Office printing, with corrections.)
2. Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In 2nd Internat. Symp. Information Theory, eds B. N. Petrov and F. Csaki, Akademiai Kiado, Budapest, pp. 261-281.
3. Akaike, H. (1974). A new look at the statistical model identification. IEEE Trans. Automatic Control 19, 716-723.
4. Aki, K. (1989). Ideal probabilistic earthquake prediction. Tectonophysics 169, 197-198.
5. Bremaud, P. (1981). Point Processes and Queues: Martingale Dynamics. Springer, NewYork.
6. Csiszar, I. (1969). On generalized entropy. Studia Sci. Math. Hung. 4, 401-419.
7. Daley, D. J. and Vere-Jones, D. (1988). An Introduction to The Theory of Point Processes. Springer, New York.
8. Daley, D. J. and Vere-Jones, D. (2003). An Introduction to The Theory of Point Processes, Vol. I, Elementary Theory and Methods, 2nd edn. Springer, New York.
9. Fritz, J. (1969). Entropy of point processes. Studia Sci. Math. Hung. 4, 389-399.
10. Fritz, J. (1973). An approach to the entropy of point processes. Periodica Math. Hung. 3, 73-83.
11. Grigelionis, B. (1974). The representation by stochastic integrals of square integrable martingales. Litovsk. Mat. Sb. 14, 53-69, 233-234 (in Russian).
12. Grigelionis, B. (1975). Stochastic point processes and martingales. Litovsk. Mat. Sb. 15, 101-114, 227-228 (in Russian).
13. Imoto, M. (2000). A quality factor of earthquake probability models in terms of mean information gain. Zesin 53, 79-81.
14. Jacod, J. and Shiryaev, A. N. (1987). Limit Theorems for Stochastic Processes. Springer, Berlin.
15. Kagan, Y. Y and Knopoff, L. (1977). Earthquake risk prediction as a stochastic process. Phys. Earth Planet. Interiors 14, 97-108.
16. Kallenberg, O. (1986). Random Measures, 4th edn. Akademie Verlag, Berlin.
17. Liptser, R. S. and Shiryaev, A. N. (2001). Statistics of Random Processes, Vol. II, Applications (Appl. Math. 5), 2nd edn. Springer, Berlin.
18. Macchi, O. (1975). The coincidence approach to stochastic point processes. Adv. Appl. Prob. 7, 83-122.
19. McFadden, J. (1965). The entropy of a point process. J. Soc. Ind. Appl. Math. 13, 988-994.
20. Papangelou, F. (1978). On the entropy rate of stationary point processes. Z. Wahrscheinlichkeitsth. 44, 191-211.
21. Renyi, A. (1959). On the dimension and entropy of probability distributions. Acta Math. Acad. Sci. Hung. 10, 193-215.
22. Renyi, A. (1960). Dimension, entropy and information. In Trans. 2nd Prague Conf. Inf. Theory, Publishing House of the Czechoslovak Academy of Science, Prague, pp. 545-556.
23. Rudemo, M. (1964). Dimension and entropy for a class of stochastic processes. Magyar Tud. Akad. Mat. Kutato Int. Kozl. 9, 73-87.
24. Vere-Jones, D. (1998). Probability and information gain for earthquake forecasting. Comput. Seismol. 30, 248-263.