Is it correct to apply likelihood for making predictions?

[HSID]

hi folks,
I quickly read through the implementations and found that the DefaultPredictionStrategy has already taken the noise of likelihood into consideration to calculate the posterior distribution.
However, in the exact GP sample code, the predicted distribution is "likelihood(model(test_x))", which seems like adding the noise term two times to me.

[Balandat]

As you said, the prediction strategy will properly take the noise of the likelihood into account when computing the posterior distribution. For prediction, model(test_x) provides the posterior over the latent function values. Applying the likelihood to that posterior gives you the posterior predictive, i.e. the distribution over the observed values (internally this is done by just by adding the observation noise to the diagonal of the posterior covariance).