Linear parametrization: `a + b(x - mu) `

[stijn]

@Jacob_Moore

As I understand it, this would have the effect of linking mu_Y muYmu_Y to mu_X muXmu_X ; in other words, if you supply the global average X, you get the global average Y in response. (I might be wrong here!)

You are not wrong here but this is not the result of the parametrization, it is the result of the linear model. If the linear model is correct, y = \mu_y is expected to happen when x = \mu_x. The parametrization is mainly to ease the interpretation of a and sampling efficiency as you say.