Lo, Albert Y. Bayesian nonparametric statistical inference for Poisson point processes. (English) Zbl 0482.62078 Z. Wahrscheinlichkeitstheor. Verw. Geb. 59, 55-66 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 25 Documents MSC: 62M09 Non-Markovian processes: estimation 60G55 Point processes (e.g., Poisson, Cox, Hawkes processes) 62F15 Bayesian inference 60G57 Random measures 62G05 Nonparametric estimation Keywords:intensity measure; weighted gamma prior probability; Skorokhod topology PDFBibTeX XMLCite \textit{A. Y. Lo}, Z. Wahrscheinlichkeitstheor. Verw. Geb. 59, 55--66 (1982; Zbl 0482.62078) Full Text: DOI References: [1] Aalen, O., Nonparametric inference for a family of counting processes, Ann. Statist., 6, 701-726 (1978) · Zbl 0389.62025 [2] Berk, R. H., Consistency a posteriori, Ann. Math. Statist., 41, 894-906 (1970) · Zbl 0214.45703 [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 [4] Brown, M.; Lewis, P. A.W., Statistical analysis of non-homogeneous Poisson point processes, Stochastic Point Processes (1972), New York: Wiley Interscience, New York · 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 [6] Dawid, A. P., On the limiting normality of posterior distributions, Proc. Cambridge Phil. Soc., 67, 625-633 (1970) · Zbl 0211.50802 [7] Doksum, K., Tailfree and neutral random probabilities and their posterior distributions, Ann. Probability, 2, 183-201 (1974) · Zbl 0279.60097 [8] Doob, J., Application of the theory of martingales, 22-28 (1949), Paris: Coll. Int. du CNRS, Paris · Zbl 0041.45101 [9] Dykstra, R. L.; Laud, P., A Bayesian nonparametric approach to reliability, Ann. Statist., 9, 356-367 (1981) · Zbl 0469.62077 [10] Fabius, J., Asymptotic behavior of Bayes’ estimates, Ann. Math. Statist., 35, 846-856 (1964) · Zbl 0137.12604 [11] Ferguson, T., A Bayesian analysis of some nonparametric problems, Ann. Statist., 1, 209-230 (1973) · Zbl 0255.62037 [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 [13] Harris, T., Counting measures monotone random set funcitons, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 10, 102-119 (1968) · Zbl 0165.18902 [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 (1976), Berlin: Akademie-Verlag and Academic Press, Berlin · Zbl 0345.60032 [16] Le Cam, L., Les propriétés asymptotiques des solutions des Bayes, Publ. Inst. Statist. Univ. Paris, 7, 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 Statistics, 1, 277-330 (1953) · Zbl 0052.15404 [18] Lewis, P. A.W.; Lewis, P. A.W., Recent results in the statistical analysis of univariate point processes, Stochastic Point Processes (1972), New York: Wiley-Interscience, New York · Zbl 0263.62056 [19] Lo, A. Y., Some contributions to Bayesian nonparametric statistical inference, Ph.D. dissertation (1978), Berkeley: University of California, Berkeley [20] Lo, A.Y.: On a class of Bayesian nonparametric estimates: II. Rate function estimates. [To appear (1978)] · Zbl 0716.62043 [21] Loéve, M., Probability Theory (1963), New York: D. Van Nostrand, New York · Zbl 0108.14202 [22] Matthes, K.; Kerstan, J.; Mecke, J., Infinitely Divisible Point Process (1978), New York: Wiley, New York · Zbl 0521.60056 [23] Prohorov, Yu. V., Convergence of random processes and limit theorems in probability theory, Theor. Probability Appl., 1, 157-214 (1956) [24] Walker, A. M., On the asymptotic behavior of posterior distributions, J. Roy. Statist. Soc. B, 31, 80-88 (1969) · Zbl 0176.48901 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.