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Bayesian nonparametric statistical inference for Poisson point processes. (English) Zbl 0482.62078

MSC:
62M09 Non-Markovian processes: estimation
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
62F15 Bayesian inference
60G57 Random measures
62G05 Nonparametric estimation
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[1] Aalen, O.: Nonparametric inference for a family of counting processes. Ann. Statist.6, 701-726 (1978) · Zbl 0389.62025 · doi:10.1214/aos/1176344247
[2] Berk, R.H.: Consistency a posteriori. Ann. Math. Statist.41, 894-906 (1970) · Zbl 0214.45703 · doi:10.1214/aoms/1177696967
[3] Bickel, P.J., Wichura, M.J.: Convergence criteria for multiparameters stochastic processes and some applications. Ann. Math. Statist.42, 1656-1670 (1971) · Zbl 0265.60011 · doi:10.1214/aoms/1177693164
[4] Brown, M.: Statistical analysis of non-homogeneous Poisson point processes. InStochastic Point Processes. P.A.W. Lewis, ed. New York: Wiley Interscience 1972 · Zbl 0263.62057
[5] Clevenson, M.L., Zidek, J.W.: Bayes linear estimators of the intensity function of the nonstationary Poisson process. J. Amer. Statist. Assoc.72, 112-120 (1977) · Zbl 0366.62007 · doi:10.2307/2286918
[6] Dawid, A.P.: On the limiting normality of posterior distributions. Proc. Cambridge Phil. Soc.67, 625-633 (1970) · Zbl 0211.50802 · doi:10.1017/S0305004100045953
[7] Doksum, K.: Tailfree and neutral random probabilities and their posterior distributions. Ann. Probability2, 183-201 (1974) · Zbl 0279.60097 · doi:10.1214/aop/1176996703
[8] Doob, J.: Application of the theory of martingales. Coll. Int. du CNRS. Paris, 22-28 (1949) · Zbl 0041.45101
[9] Dykstra, R.L., Laud, P.: A Bayesian nonparametric approach to reliability. Ann. Statist.9, 356-367 (1981) · Zbl 0469.62077 · doi:10.1214/aos/1176345401
[10] Fabius, J.: Asymptotic behavior of Bayes’ estimates. Ann. Math. Statist.35, 846-856 (1964) · Zbl 0137.12604 · doi:10.1214/aoms/1177703584
[11] Ferguson, T.: A Bayesian analysis of some nonparametric problems. Ann. Statist.1, 209-230 (1973) · Zbl 0255.62037 · doi:10.1214/aos/1176342360
[12] Freedman, D.A.: On the asymptotic behavior of Bayes estimates in the discrete case. Ann. Math. Statist.34, 1386-1403 (1963) · Zbl 0137.12603 · doi:10.1214/aoms/1177703871
[13] Harris, T.: Counting measures monotone random set funcitons. Z. Wahrscheinlichkeitstheorie verw. Gebiete10, 102-119 (1968) · Zbl 0165.18902 · doi:10.1007/BF00531844
[14] Johnson, R.A.: Asymptotic expansions associated with posterior distributions. Amer. Math. Soc.41, 851-864 (1970) · Zbl 0204.53002
[15] Kallenberg, O.: Random Measures. Berlin: Akademie-Verlag and Academic Press 1976 · Zbl 0345.60032
[16] Le Cam, L.: Les propriétés asymptotiques des solutions des Bayes. Publ. Inst. Statist. Univ. Paris7, 17-35 (1958) · Zbl 0084.14303
[17] Le Cam, L.: On some asymptotic properties of maximum likelihood estimates and related Bayes estimates. University of California Public Statistics1, 277-330 (1953)
[18] Lewis, P.A.W.: Recent results in the statistical analysis of univariate point processes. In Stochastic Point Processes, P.A.W. Lewis, ed., New York: Wiley-Interscience (1972) · Zbl 0263.62056
[19] Lo, A.Y.: Some contributions to Bayesian nonparametric statistical inference. Ph.D. dissertation, University of California, Berkeley (1978)
[20] Lo, A.Y.: On a class of Bayesian nonparametric estimates: II. Rate function estimates. [To appear (1978)]
[21] Loéve, M.: Probability Theory, 3rd ed. New York: D. Van Nostrand. 1963
[22] Matthes, K., Kerstan, J., Mecke, J.: Infinitely Divisible Point Process. New York: Wiley 1978 · Zbl 0383.60001
[23] Prohorov, Yu.V.: Convergence of random processes and limit theorems in probability theory. Theor. Probability Appl.1, 157-214 (1956) · doi:10.1137/1101016
[24] Walker, A.M.: On the asymptotic behavior of posterior distributions. J. Roy. Statist. Soc. B31, 80-88 (1969) · Zbl 0176.48901
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