Definition of Term: Basis functions¶

The mean function of an emulator, \(m(x)\), expresses the global behaviour of the computer model and can be written in a variety of forms as described in the alternatives page on emulator prior mean function (AltMeanFunction). When the mean function takes a linear form it can be expressed as \(m(x)=\beta^Th(x)\) where \(h(x)\) is a \(q\)-vector of known basis functions of \(x\) which describe global features of the simulator’s behaviour and \(\beta\) is a vector of unknown coefficients.

The task of specifying appropriate forms for \(h(x)\) is addressed in the alternatives page on basis functions for the emulator mean (AltBasisFunctions).