  Gaussian process is a very promising novel technology that has been applied
to both the regression problem and the classification problem. While for the
regression problem it yields simple exact solutions, this is not the case for
the classification problem, because we encounter intractable integrals. In this
paper we develop a new derivation that transforms the problem into that of
evaluating the ratio of multivariate Gaussian orthant integrals. Moreover, we
develop a new Monte Carlo procedure that evaluates these integrals. It is based
on some aspects of bootstrap sampling and acceptancerejection. The proposed
approach has beneficial properties compared to the existing Markov Chain Monte
Carlo approach, such as simplicity, reliability, and speed.
