  In this paper, we investigate Gaussian process modeling with input location
error, where the inputs are corrupted by noise. Here, the best linear unbiased
predictor for two cases is considered, according to whether there is noise at
the target unobserved location or not. We show that the mean squared prediction
error converges to a non-zero constant if there is noise at the target
unobserved location, and provide an upper bound of the mean squared prediction
error if there is no noise at the target unobserved location. We investigate
the use of stochastic Kriging in the prediction of Gaussian processes with
input location error, and show that stochastic Kriging is a good approximation
when the sample size is large. Several numeric examples are given to illustrate
the results, and a case study on the assembly of composite parts is presented.
Technical proofs are provided in the Appendix.
