I was reading this paper related to gaussian processes http://ipg.epfl.ch/~seeger/lapmalmainweb/papers/bayesgp-tut.pdf. I didn't get how they derived the posterior of the gaussian process given some observed data
I understand that y follows normal having mean u and std $\epsilon$. Both y and u have normal distribution with mean 0. Only the covariance is different in the case of y an u.Can anyone please explain how the posterior was derived. I didn't get how the $K$ part came in the mean of the posterior and the covariance of the posterior
Well
u ~ 0 K K_uy
y ~ 0 K_uy K+$\sigma^2$
I didn't get how the part K_uy is calculated. They have placed it to be K. I am not sure why. Clarificiations?
Also can you explain how the prediction process is derived. I know the integration makes sense. But how did they get the final expression?
