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

Genyuan Li, Herschel Rabitz

Research output: Contribution to journalArticle

5 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)2052-2073
Number of pages22
JournalJournal of Mathematical Chemistry
Volume52
Issue number8
DOIs
StatePublished - Jan 1 2014

All Science Journal Classification (ASJC) codes

  • Chemistry(all)
  • Applied Mathematics

Keywords

  • Correlated variables
  • HDMR
  • Sensitivity analysis

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