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GPs: defining distributions over functions instead of points.

It’s an interesting stretch to think about functions as random variables.

No problem. Exactly. I think that example is misleading and shouldn’t be used against R2 to undermine its credibility for predictive performance evaluation.

You won’t get different r2 if you only change the unit of y (e.g. height). Your regression coefficients will change and the r2 remains unchanged.

Goodness of prediction and goodness of detection of the detectable signal are two different things. You can do a good job in finding the true underlaying function and yet fail miserably in having a good prediction model.

I disagree, that shows why r2 is better than mse. The second example has significantly weaker signal and r2 shows that while mse doesn’t. 1 cm error in predicting a human’s height is very good while it’s rubbish for predicting an ant’s height (same mse, different context). R2 reflects the context

How is it not good measure of predictive accuracy?