Saddlepoint Approximations to the Moments of Multitype Age-Dependent Branching Processes, with Applications

Authors

  • O. Hyrien,

    Corresponding author
    1. Department of Biostatistics and Computational Biology, University of Rochester Medical Center, 601 Elmwood Avenue, Rochester, New York 14642, U.S.A.
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  • R. Chen,

    1. Department of Biostatistics and Computational Biology, University of Rochester Medical Center, 601 Elmwood Avenue, Rochester, New York 14642, U.S.A.
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  • M. Mayer-Pröschel,

    1. Department of Biomedical Genetics, University of Rochester Medical Center, 601 Elmwood Avenue, Rochester, New York 14642, U.S.A.
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  • M. Noble

    1. Department of Biomedical Genetics, University of Rochester Medical Center, 601 Elmwood Avenue, Rochester, New York 14642, U.S.A.
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email: Ollivier_Hyrien@urmc.rochester.edu

Abstract

Summary This article proposes saddlepoint approximations to the expectation and variance–covariance function of multitype age-dependent branching processes. The proposed approximations are found accurate, easy to implement, and much faster to compute than by simulating the process. Multiple applications are presented, including the analyses of clonal data on the generation of oligodendrocytes from their immediate progenitor cells, and on the proliferation of Hela cells. New estimators are also constructed to analyze clonal data. The proposed methods are finally used to approximate the distribution of the generation, which has recently found several applications in cell biology.

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