Inconsistency in rational kernels

[devmotion]

Since RationalQuadraticKernel and GammaRationalQuadraticKernel are grouped together in the documentation and refer to each other in the docstring, I noticed an inconsistency in the implementation: RationalQuadraticKernel includes an additional factor of 2 in the denominator whereas GammaRationalQuadraticKernel doesn't. Is there a reason for this behaviour or is this a bug, @willtebbutt?

With the additional factor of 2 in the denominator, the more general kernel would yield the same kernel with its default values whereas currently the inputs have to be scaled. On the other hand, one would lose the property that the GammaExponentialKernel is the limit of the GammaRationalQuadraticKernel as alpha goes to infinity. But the name "GammaRationalQuadraticKernel" seems to indicate that it is more closely related to the RationalQuadraticKernel...

Maybe

• one should rename GammaRationalQuadraticKernel to GammaRationalKernel now that the factor 2 in the exponent is removed
• add an explicit RationalKernel for the case gamma=1 of the GammaRationalQuadraticKernel, which yields an ExponentialKernel as alpha goes to infinity
• change the default value of gamma of the GammaRationalKernel to 1, such that it is a generalization of RationalKernel instead of RationalQuadraticKernel, similar to the relation of ExponentialKernel and GammaExponentialKernel

Then everything would be consistent with the setup in the limit for alpha=\infty.

What do you think, @willtebbutt?

Originally posted by @devmotion in #236 (comment)