This paper deals with two subjects. First, we will show how support vector machine (SVM) regression problem can be solved as the maximum a posteriori prediction in the Bayesian framework. The second part describes an approximation technique that is useful in performing calculations for SVMs based on the mean eld algorithm which was originally proposed in Statistical Physics of disordered systems. One advantage is that it handle posterior averages for Gaussian process which are not analytically tractable. c © 2002 Elsevier Science B.V. All rights reserved.