On Bayesian inference about the smoothness parameter in Gaussian Matern random fields by Victor De Oliveira

Nice technical derivation of a default prior for the smoothness parameter.
Identifiability (or lack thereof) of the smoothness and range parameters.
This should get worse as the design becomes more sparse (i.e., “roughness” and “wiggliness” begin to look very similar)
Why do we care about the precise number of derivatives?
How should we normalize the measurements to make the information values comparable?
Role of the measurement error and possible need for a nugget.
The error variance is the product of the GP variance and a scaling factor.
Is this choice dictated by modeling considerations of computational convenience?
Role of available covariates.
Do they really need to be measured on a regular grid? What if they are not?
Trade off between modeling the mean response and the correlation structure.
This could also lead to issues with identifiability, necessitating restrictions on the smoothness of the mean function relative to the smoothness of the GP covariance.
Computer models output vs. real data
Compare the predictive performance to that of a Bayesian method where the range parameter has a full posterior and the smoothness parameter has a plug-in estimate (or is fixed a priori)
Need for data analysis.

Points for Discussion