  This paper is motivated by a computer experiment conducted for optimizing
residual stresses in the machining of metals. Although kriging is widely used
in the analysis of computer experiments, it cannot be easily applied to model
the residual stresses because they are obtained as a profile. The high
dimensionality caused by this functional response introduces severe
computational challenges in kriging. It is well known that if the functional
data are observed on a regular grid, the computations can be simplified using
an application of Kronecker products. However, the case of irregular grid is
quite complex. In this paper, we develop a Gibbs sampling-based expectation
maximization algorithm, which converts the irregularly spaced data into a
regular grid so that the Kronecker product-based approach can be employed for
efficiently fitting a kriging model to the functional data.

Methodology;Computation