  Stein [Statist. Sci. 4 (1989) 432--433] proposed the Mat\'{e}rn-type Gaussian
random fields as a very flexible class of models for computer experiments. This
article considers a subclass of these models that are exactly once mean square
differentiable. In particular, the likelihood function is determined in closed
form, and under mild conditions the sieve maximum likelihood estimators for the
parameters of the covariance function are shown to be weakly consistent with
respect to fixed-domain asymptotics.
