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Analytical HDMR formulas for functions expressed as quadratic polynomials with a multivariate normal distribution

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Abstract

High Dimensional Model Representation (HDMR) is a general set of quantitative model assessment and analysis tools for systems with many variables. A general formulation for the HDMR component functions with independent and correlated variables was obtained previously. Since the HDMR component functions generally are coupled to one another and involve multi-dimensional integrals, explicit formulas for the component functions are not available for an arbitrary function with an arbitrary probability distribution amongst their variables. This paper presents analytical formulas for the HDMR component functions and the corresponding sensitivity indexes for the common case of a function expressed as a quadratic polynomial with a multivariate normal distribution over its variables. This advance is important for practical applications of HDMR with correlated variables.

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Acknowledgments

Support for this work was provided by ONR with account number N00014-11-1-0716.

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Authors and Affiliations

  1. Department of Chemistry, Princeton University, Princeton, NJ,  08544, USA

    Genyuan Li & Herschel Rabitz

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  1. Genyuan Li
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  2. Herschel Rabitz
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Correspondence to Herschel Rabitz.

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Li, G., Rabitz, H. Analytical HDMR formulas for functions expressed as quadratic polynomials with a multivariate normal distribution. J Math Chem 52, 2052–2073 (2014). https://doi.org/10.1007/s10910-014-0365-6

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  • DOI: https://doi.org/10.1007/s10910-014-0365-6

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