[murbard2]

Because the prior on your parameters smooths out the prediction.

Most cookbook techniques such as ridge regressions, cross-validation, etc have a Bayesian interpretation as a prior on the parameter.

Bayesian techniques allow you to use all the data available.

That said, sometimes they are computationally expensive, and it's better to approximate them by using a test set.

[moultano]

Unless you have an infinite regress on priors for your priors, and uncomputable Komolgorov penalties on the structure of your model, I think you need a test set. (This means you need a test set.)

[ced]

There's an interesting chapter in MacKay's book on Occam's razor. I'm not sure how I feel about it, but it's very thought-provoking.

[GFK_of_xmaspast]

If your priori are that strong, why bother with the data?

[Totient]

You don't need a validation set. I'm pretty sure you still want a test set.