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Filtering the histories of a partially observed marked point process

Author

Listed:
  • Arjas, Elja
  • Haara, Pentti
  • Norros, Ikka

Abstract

We consider a situation in which the evolution of an 'underlying' marked point process is of interest, but where this process is not directly observable. Instead, we assume that another marked point process, which is fully determined by the underlying process, can be observed. The problem is then the estimation, at any given time t, of the underlying development so far, given the corresponding observations. The solution, in the sense of a conditional distribution of the underlying pre-t history, is shown to satisfy a recursive filter formula. Sufficient conditions for the uniqueness of the solution are given. Two non-trivial examples are considered in detail.

Suggested Citation

  • Arjas, Elja & Haara, Pentti & Norros, Ikka, 1992. "Filtering the histories of a partially observed marked point process," Stochastic Processes and their Applications, Elsevier, vol. 40(2), pages 225-250, March.
    • Handle: RePEc:eee:spapps:v:40:y:1992:i:2:p:225-250
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    Citations

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    Cited by:

    1. Brandejsky, Adrien & de Saporta, Benoîte & Dufour, François, 2013. "Optimal stopping for partially observed piecewise-deterministic Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3201-3238.
    2. Erhan Bayraktar & Michael Ludkovski, 2010. "Inventory management with partially observed nonstationary demand," Annals of Operations Research, Springer, vol. 176(1), pages 7-39, April.
    3. Jin Feng, 2002. "A Stochastic Filtering Approach To Survival Analysis," Statistical Inference for Stochastic Processes, Springer, vol. 5(1), pages 23-53, January.
    4. Jukka Corander, 2023. "A conversation with Elja Arjas (Helsinki, November 2021 and March 2022)," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 3-12, March.
    5. Vanessa Didelez, 2008. "Graphical models for marked point processes based on local independence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 245-264, February.
    6. Ceci, Claudia & Gerardi, Anna, 1998. "Partially observed control of a Markov jump process with counting observations: equivalence with the separated problem," Stochastic Processes and their Applications, Elsevier, vol. 78(2), pages 245-260, November.
    7. Bayraktar, Erhan & Ludkovski, Michael, 2009. "Sequential tracking of a hidden Markov chain using point process observations," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 1792-1822, June.
    8. Browne, Sid & Bunge, John, 1995. "Random record processes and state dependent thinning," Stochastic Processes and their Applications, Elsevier, vol. 55(1), pages 131-142, January.

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