Variance propagation in cubing.py

[MOwers]

Hi Pablo,

I think that there is an error in the interpolate_fibre function where you propagate variance. In the line:

    cube_var[wl_range: wl_range + spectral_window, rows_min:rows_max - 1, cols_min:cols_max - 1] += (
            fib_variance[wl_range: wl_range + spectral_window, np.newaxis, np.newaxis]
            * w)

it should be w**2

Cheers,
Matt.

[PabloCorcho]

Hi Matt. Thanks for letting me know! I will start fixing this issue along with the refactoring of the cubing process.

[PabloCorcho]

I have been checking this and I would swear the above expression is correct... The variance is interpolated in the cube using the a kernel-based weight (w) in the same way as the intensity, so the contribution from a single RSS to a cube is defined as:

$$ I_{cube}(\lambda, x,y) = \int\int I_{RSS}^{i}(\lambda, x', y') \cdot K(x - y', y - y')\ dx'dy' $$

$$ var_{cube}(\lambda, x,y) = \int\int var_{RSS}^{i}(\lambda, x', y') \cdot K(x - y', y - y')\ dx'dy' $$

where $K(x - y', y - y')\ dx'dy'$ corresponds to the variable w and ($x',\ y'$) is the location of a fibre in the pixel space. This preserves the integrated variance and intensity (if the domain of $x',\ y'$ is contained within $x,\ y$). Maybe I am missing something. We can discuss this in a telecon.

[MOwers]

Hi Pablo, This is not the standard method for propagating variance -- check the Law et al. paper for MaNGA, for example ( https://ui.adsabs.harvard.edu/abs/2016AJ....152...83L/abstract). When we compared the variance in the cubes using your propagation against a simple method of checking the scatter in the residuals we found them to be very different. Correcting the code to use standard variance propagation solved this problem. Cheers, Matt.

…

On Fri, 10 May 2024 at 23:40, CorchoCaballero ***@***.***> wrote: I have been checking this and I would swear the above expression is correct... The variance is interpolated in the cube using the a kernel-based weight (w) in the same way as the intensity, so the contribution from a single RSS to a cube is defined as: $$ I_{cube}(\lambda, x,y) = \int\int I_{RSS}^{i}(\lambda, x', y') \cdot K(x - y', y - y')\ dx'dy' $$ $$ var_{cube}(\lambda, x,y) = \int\int var_{RSS}^{i}(\lambda, x', y') \cdot K(x - y', y - y')\ dx'dy' $$ where $K(x - y', y - y')\ dx'dy'$ corresponds to the variable w and ($x',\ y'$) is the location of a fibre in the pixel space. This preserves the integrated variance and intensity (if the domain of $x',\ y'$ is contained within $x,\ y$). Maybe I am missing something. We can discuss this in a telecon. — Reply to this email directly, view it on GitHub <#412 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AMGQENKQR7V4IJ4J32LZOB3ZBTE5RAVCNFSM6AAAAABHPUD4CSVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDCMBUGYZTCMZXHE> . You are receiving this because you authored the thread.Message ID: ***@***.***>

-- Matt Owers School of Mathematical and Physical Sciences, Macquarie University ph: +61 2 9850 8910