[pjin]

Hmm, so gaussian distributions are easy to use and ubiquitous and all (they're the basis functions used in SVM), except that I don't see any reason for them to be priors here. But since 2012 > 2008 I feel like I'm obligated (and I'm semi-trolling) to point out the obvious about lazy assumptions based on "flexibility and tractability", which is that they can implode hilariously in your face. C.f. the financial crisis.

[1] http://econometricsense.blogspot.com/2011/03/copula-function...

[bayesregressor]

I think you're confusing the Gaussian "process" used in Bayesian optimization with a standard Gaussian distribution. They are very different things - as are Gaussian copulas and what is referred to as the 'Gaussian kernel' (which is not actually a distribution at all) in the SVM. The Gaussian process is a distribution over functions, the properties of which are governed by the covariance function - so the prior over the function, or the assumption about its complexity and form, is determined by the choice of covariance function. Of course it is very important to choose a prior that corresponds to the functional form you are interested in, which is actually discussed and empirically validated in the literature referred to in that post. It's a bit ironic that you are claiming to point out the dangers of making lazy assumptions by doing exactly that.