  Gaussian processes models are widely adopted for
nonparameteric/semi-parametric modeling. Identifiability issues occur when the
mean model contains polynomials with unknown coefficients. Though resulting
prediction is unaffected, this leads to poor estimation of the coefficients in
the mean model, and thus the estimated mean model loses interpretability. This
paper introduces a new Gaussian process model whose stochastic part is
orthogonal to the mean part to address this issue. This paper also discusses
applications to multi-fidelity simulations using data examples.
