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Bayesian estimation of ordinary differential equation models when the likelihood has multiple local modes

Author

Listed:
  • Liu Baisen

    (School of Statistics, Dongbei University of Finance and Economics, Dalian, 116025, P. R. China)

  • Wang Liangliang

    (Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, BC, V5A1S6, Canada)

  • Cao Jiguo

    (Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, BC, V5A1S6, Canada)

Abstract

Ordinary differential equations (ODEs) are popularly used to model complex dynamic systems by scientists; however, the parameters in ODE models are often unknown and have to be inferred from noisy measurements of the dynamic system. One conventional method is to maximize the likelihood function, but the likelihood function often has many local modes due to the complexity of ODEs, which makes the optimizing algorithm be vulnerable to trap in local modes. In this paper, we solve the global optimization issue of ODE parameters with the help of the Stochastic Approximation Monte Carlo (SAMC) algorithm which is shown to be self-adjusted and escape efficiently from the “local-trapping” problem. Our simulation studies indicate that the SAMC method is a powerful tool to estimate ODE parameters globally. The efficiency of SAMC method is demonstrated by estimating a predator-prey ODEs model from real experimental data.

Suggested Citation

  • Liu Baisen & Wang Liangliang & Cao Jiguo, 2018. "Bayesian estimation of ordinary differential equation models when the likelihood has multiple local modes," Monte Carlo Methods and Applications, De Gruyter, vol. 24(2), pages 117-127, June.
    • Handle: RePEc:bpj:mcmeap:v:24:y:2018:i:2:p:117-127:n:4
    DOI: 10.1515/mcma-2018-0010
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    References listed on IDEAS

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