The conditional probability of the continuous x now has another form, however.
pGB(x|h)=pGB(x,h)pGB(h)=1ZGBe−||x−a2σ||2+bTh+(xσ2)TWh1ZGBebTh∏Mi√2πσ2ie2aiwTi∗h+(wTi∗h)22σ2i=M∏i1√2πσ2ie−(xi−ai)22σ2i+xiwTi∗h2σ2ie2aiwTi∗h+(wTi∗h)22σ2i=M∏i1√2πσ2ie−x2i−2aixi+a2i−2xiwTi∗h2σ2ie2aiwTi∗h+(wTi∗h)22σ2i=M∏i1√2πσ2ie−x2i−2aixi+a2i−2xiwTi∗h+2aiwTi∗h+(wTi∗h)22σ2i=M∏i1√2πσ2ie−(xi−bi−wTi∗h)22σ2i=M∏iN(xi|bi+wTi∗h,σ2i)⇒pGB(xi|h)=N(xi|bi+wTi∗h,σ2i).