Editing Sensitivity analysis (section)

=== High-dimensional model representations (HDMR) ===
A [[high-dimensional model representation]] (HDMR)<ref>{{cite journal | last1 = Li | first1 = G. | last2 = Hu | first2 = J. | last3 = Wang | first3 = S.-W. | last4 = Georgopoulos | first4 = P. | last5 = Schoendorf | first5 = J. | last6 = Rabitz | first6 = H. | year = 2006 | title = Random Sampling-High Dimensional Model Representation (RS-HDMR) and orthogonality of its different order component functions | journal = Journal of Physical Chemistry A | volume = 110 | issue = 7| pages = 2474–2485 | doi=10.1021/jp054148m| pmid = 16480307 | bibcode = 2006JPCA..110.2474L }}</ref><ref>{{cite journal | last1 = Li | first1 = G. | year = 2002 | title = Practical approaches to construct RS-HDMR component functions | journal = Journal of Physical Chemistry | volume = 106 | issue = 37| pages = 8721–8733 | doi = 10.1021/jp014567t | bibcode = 2002JPCA..106.8721L }}</ref> (the term is due to H. Rabitz<ref>{{cite journal | last1 = Rabitz | first1 = H | year = 1989 | title = System analysis at molecular scale | journal = Science | volume = 246 | issue = 4927| pages = 221–226 | doi=10.1126/science.246.4927.221| pmid = 17839016 | bibcode = 1989Sci...246..221R| s2cid = 23088466 }}</ref>) is essentially an emulator approach, which involves decomposing the function output into a linear combination of input terms and interactions of increasing dimensionality. The HDMR approach exploits the fact that the model can usually be well-approximated by neglecting higher-order interactions (second or third-order and above). The terms in the truncated series can then each be approximated by e.g. polynomials or splines (REFS) and the response expressed as the sum of the main effects and interactions up to the truncation order. From this perspective, HDMRs can be seen as emulators which neglect high-order interactions; the advantage is that they are able to emulate models with higher dimensionality than full-order emulators.