Also, we used to have a noise variance of 1.e4 (called sky_level).  I like to avoid 1's in examples (and tests) whenever possible, since it can allow confusion between reciprocals.  I think I'd recommend leaving the variance as 1.e4, with maybe some text pointing out that it is similar to having a sky_level of 1.e4, but now with an associated correlation.  But at least something != 1.