Combining estimated errors (galaxy properties, of the observ

[JeanTate]

Suppose I determine that the position angle (PA) of a galaxy, in one band - observed by SDSS - is -85.4 ± 8.9°, and is 84.7 ± 10.9° in another. Assuming - for now - that the errors have a Gaussian distribution, and that the "±" numbers are 1σ, how do I go about determining if the two (band) PAs are the same "within 1σ"? (Actually it's more like the binary "are the data consistent with the hypothesis that ...?")

PA is nice an linear, and - modulo something subtle and potentially interesting (either an SDSS systematic or weak gravitational lensing, say) - the PAs will be distributed evenly over the interval (-90, 90), a distribution which wraps around (i.e. -90 = 90).

Suppose I determine that the axis ratio of a galaxy ("ab"), in one band is 0.73±0.05, and 0.82±0.04 in another. And I want to ask a similar question.

In this case, ab isn't distributed evenly over (0, 1) - at least I don't think it is - and certainly doesn't 'wrap around'. Does that make the calculations needed to answer the question different? (again, assume no systematics).

Next: effective radius (r_e), 11.6±0.4 and 9.2±0.4 say (unit? pixels, but it doesn't matter, does it?).

In this case, the question becomes a lot more complicated, does it not?

I mean, r_e carries with it the value of n, the Sérsic profile index (or some other model), which is not - necessarily - the same for both bands. And the distribution is far from linear, isn't it? What is needed to do the calculations in cases like this?

[JeanTate]

In a different thread, in this same section/board, Chris Peterson mentioned 'bounded errors', and said that there are clever ways to handle these.

That would seem to be pertinent to this, long dormant, thread too.

So I'm bumping it.