Difficulty understanding the different ways of using a prior on the mean

[ThGbay]

Hello everyone,

I would like to add a prior on the mean. This prior is a Gaussian Process (GP) ConstantMean(). In other words, as a prior, I give a new GP the mean of another GP.

I've studied the documentation for adding a prior and I'm having trouble understanding the differences between the ways of adding a prior.

For example, in the "gpytorch.means.ConstantMean" subclass, there's a "constant_prior" parameter taking an argument of type "gpytorch.priors.Prior". This returns a "log-probability of the parameter value under the prior".

1 - Here I'm having trouble using "constant_prior" correctly with "gpytorch.priors.Prior", considering the parameters required by gpytorch.priors.Prior : batch_shape and event_shape. Do you have an example somewhere ?

https://docs.gpytorch.ai/en/stable/priors.html

2 - What's the difference between using the 1-approach above and using "register_prior" in the "gpytorch.Module" class? Or even "register parameter"?

https://docs.gpytorch.ai/en/stable/module.html#gpytorch.Module.register_prior

Thank you for your help,