Definition of Term: NuggetΒΆ

A covariance function \(v(x,x^\prime)\) expresses the covariance between the outputs of a simulator at input configurations \(x\) and \(x^\prime\). When \(x=x^\prime\), \(v(x,x)\) is the variance of the output at input \(x\). A nugget is an additional component of variance when \(x=x^\prime\). Technically this results in the covariance function being a discontinuous function of its arguments, because \(v(x,x)\) does not equal the limit as \(x^\prime\) tends to \(x\) of \(v(x,x^\prime)\).

A nugget may be introduced in a variance function in MUCM methods for various reasons. For instance, it may represent random noise in a stochastic simulator, or the effects of inactive inputs that are not included explicitly in the emulator. A small nugget term may also be added for computational reasons when working with a deterministic simulator.