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Estimating Equations for Density Dependent Markov Jump Processes

Author

Listed:
  • Oluseyi Odubote

    (Corteva Agriscience, Johnston, IA 50131, USA
    These authors contributed equally to this work.)

  • Daniel F. Linder

    (Medical College of Georgia, Augusta University, Augusta, GA 30912, USA
    These authors contributed equally to this work.
    Current address: 1120 15th St., Augusta, GA 30912, USA.)

Abstract

Reaction networks are important tools for modeling a variety of biological phenomena across a wide range of scales, for example as models of gene regulation within a cell or infectious disease outbreaks in a population. Hence, calibrating these models to observed data is useful for predicting future system behavior. However, the statistical estimation of the parameters of reaction networks is often challenging due to intractable likelihoods. Here we explore estimating equations to estimate the reaction rate parameters of density dependent Markov jump processes (DDMJP). The variance–covariance weights we propose to use in the estimating equations are obtained from an approximating process, derived from the Fokker–Planck approximation of the chemical master equation for stochastic reaction networks. We investigate the performance of the proposed methodology in a simulation study of the Lotka–Volterra predator–prey model and by fitting a susceptible, infectious, removed (SIR) model to real data from the historical plague outbreak in Eyam, England.

Suggested Citation

  • Oluseyi Odubote & Daniel F. Linder, 2021. "Estimating Equations for Density Dependent Markov Jump Processes," Mathematics, MDPI, vol. 9(4), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:391-:d:499966
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    References listed on IDEAS

    as
    1. Kurtz, Thomas G., 1978. "Strong approximation theorems for density dependent Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 6(3), pages 223-240, February.
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