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Optimal ANOVA-Based Emulators of Models With(out) Derivatives

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  • Matieyendou Lamboni

    (Department DFR-ST, University of Guyane, Cayenne 97346, French Guiana
    228-UMR Espace-Dev, University of Guyane, University of Réunion, IRD, University of Montpellier, 34090 Montpellier, France)

Abstract

This paper proposes new ANOVA-based approximations of functions and emulators of high-dimensional models using either available derivatives or local stochastic evaluations of such models. Our approach makes use of sensitivity indices to design adequate structures of emulators. For high-dimensional models with available derivatives, our derivative-based emulators reach dimension-free mean squared errors (MSEs) and a parametric rate of convergence (i.e., O ( N − 1 ) ). This approach is extended to cope with every model (without available derivatives) by deriving global emulators that account for the local properties of models or simulators. Such generic emulators enjoy dimension-free biases, parametric rates of convergence, and MSEs that depend on the dimensionality. Dimension-free MSEs are obtained for high-dimensional models with particular distributions from the input. Our emulators are also competitive in dealing with different distributions of the input variables and selecting inputs and interactions. Simulations show the efficiency of our approach.

Suggested Citation

  • Matieyendou Lamboni, 2025. "Optimal ANOVA-Based Emulators of Models With(out) Derivatives," Stats, MDPI, vol. 8(1), pages 1-27, March.
    • Handle: RePEc:gam:jstats:v:8:y:2025:i:1:p:24-:d:1614204
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    References listed on IDEAS

    as
    1. Kucherenko, S. & Rodriguez-Fernandez, M. & Pantelides, C. & Shah, N., 2009. "Monte Carlo evaluation of derivative-based global sensitivity measures," Reliability Engineering and System Safety, Elsevier, vol. 94(7), pages 1135-1148.
    2. Maryam Salem Alatawi & Barbara Martinucci, 2022. "On the Elementary Symmetric Polynomials and the Zeros of Legendre Polynomials," Journal of Mathematics, Hindawi, vol. 2022, pages 1-9, May.
    3. Lamboni, Matieyendou, 2021. "Derivative-based integral equalities and inequality: A proxy-measure for sensitivity analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 179(C), pages 137-161.
    4. Roustant, O. & Fruth, J. & Iooss, B. & Kuhnt, S., 2014. "Crossed-derivative based sensitivity measures for interaction screening," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 105(C), pages 105-118.
    5. Lamboni, Matieyendou & Kucherenko, Sergei, 2021. "Multivariate sensitivity analysis and derivative-based global sensitivity measures with dependent variables," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    6. Sudret, Bruno, 2008. "Global sensitivity analysis using polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 93(7), pages 964-979.
    7. Jeremy E. Oakley & Anthony O'Hagan, 2004. "Probabilistic sensitivity analysis of complex models: a Bayesian approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 751-769, August.
    8. Marc C. Kennedy & Anthony O'Hagan, 2001. "Bayesian calibration of computer models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 425-464.
    9. Sobol’, I.M. & Kucherenko, S., 2009. "Derivative based global sensitivity measures and their link with global sensitivity indices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(10), pages 3009-3017.
    10. Lamboni, Matieyendou, 2022. "Weak derivative-based expansion of functions: ANOVA and some inequalities," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 691-718.
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