Bayesian Optimal Design for Ordinary Differential Equation Models

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Overstall, Antony M.; Woods, David C.; Parker, Benjamin M.;
(2015)
  • Publisher: University of Glasgow
  • Subject:
    acm: MathematicsofComputing_NUMERICALANALYSIS

Bayesian optimal design is considered for experiments where it is hypothesised that the responses are described by the intractable solution to a system of non-linear ordinary differential equations (ODEs). Bayesian optimal design is based on the minimisation of an expec... View more
  • References (21)
    21 references, page 1 of 3

    Atkinson, A., Chaloner, K., Herzberg, A., and Juritz, J. (1993), \Experimental Designs for Properties of a Compartmental Model," Biometrics, 49, 325{337.

    Bastos, L. and O'Hagan, A. (2009), \Diagnostics for Gaussian Process Emulators," Technometrics, 51, 425{438.

    Bliznyuk, N., Ruppert, D., Shoemaker, C., Regis, R., Wild, S., and Mugunthan, P. (2008), \Bayesian calibration of computationally expensive models using optimization and radial basis function approximations." Journal of Computational and Graphical Statistics, 17, 270{294.

    Brynjarsdottir, J. and O 'Hagan, A. (2014), \Learning about physical parameters: The importance of model discrepancy," Inverse Problems, 30, 114007.

    Chkrebtii, O., Campbell, D., Girolami, M., and Calderhead, B. (2015), \Bayesian Uncertainty Quanti cation for Di erential Equations," Tech. rep., Ohio State University, USA.

    Fielding, M., Nott, D., and Liong, S. (2011), \E cient MCMC schemes for computationally expensive posterior distributions," Technometrics, 53, 16{28.

    FitzHugh, R. (1961), \Impulses and physiological states in models of nerve membrane," Biophysical Journal, 1, 445{466.

    Gotwalt, C., Jones, B., and Steinberg, D. (2009), \Fast Computation of Designs Robust to Parameter Uncertainty for Nonlinear Settings," Technometrics, 51, 88{95.

    Iserles, A. (2009), A First Course in the Numerical Analysis of Di erential Equations, Cambridge University Press.

    Jones, D., Schonlau, M., and Welch, W. (1998), \E cient global optimization of expensive black-box functions," Journal of Global Optimization, 13, 455{492.

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