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

A New Monte Carlo Based Algorithm for the Gaussian Process Classification Problem