[Docs] Unexpected behavior setting kernel priors

[ruhanaazam]

Hi, I'm interested in setting better priors on my GP kernel. I am unsure if I am setting the priors correctly. Below are two ways I have tried to set the kernel priors. I expect both to behave the same but when I fit my GP, I find that cov_module1 works significantly better than covar_module2. Is there a reason for this behavior?

lengthscale_prior = gpytorch.priors.GammaPrior(3.0, 6.0)
outputscale_prior = gpytorch.priors.GammaPrior(2.0, 0.15)

covar_module1 = ScaleKernel(
    MaternKernel(
        nu=nu,
        ard_num_dims=2,
        lengthscale_prior=lengthscale_prior,
    ),
    outputscale_prior=outputscale_prior,
)

covar_module2 = ScaleKernel(
    MaternKernel(
        nu=nu,
        ard_num_dims=2,
    ),
)
covar_module2.base_kernel.lengthscale_prior = lengthscale_prior
covar_module2.outputscale_prior = outputscale_prior

Expected Behavior
cov_module1 and cov_module2 to perform similarly when they are used to fit a SingleTaskGP.

System information
Please complete the following information:
GPyTorch: 1.10
Pytorch: 2.0.1
Ubuntu 20.04
Python: 3.10

Fyi, this is a repeat issue from pytorch/botorch#2307.

[Balandat]

You can't just assign the attribute for the prior, you need to use the register_prior() method on the GPyTorch module so that gpytorch knows to use this in the computations for the MLL. In your setup for covar_module2 I don't think that prior is ever being used.

See e.g. https://github.com/cornellius-gp/gpytorch/blob/master/gpytorch/kernels/kernel.py#L205-L207 for how this is done in the Kernel.__init__() method.