drphilmarshall
commented
12 years ago I think a toy project to infer the intrinsic ellipticity distribution simultaneously with a single applied shear would be interesting and instructive - let's coordinate with colleagues in Oxford who are interested in this problem, and related ones.
On Fri, Jul 27, 2012 at 1:32 PM, David W. Hogg reply@reply.github.com wrote:
@drphilmarshall sent this by email; let's do this!
The arguments you start to sketch, regarding hypothetical populations of highly ordered galaxies, are good for showing the reader our motivation - but in real life we work in the opposite regime, with high diversity between galaxy shapes. Most analysts' common sense is that in this case, and because of the diversity, simple averaging will be a close approximation to full-on hierarchical inference. Our aim is to investigate that assumption (not prove it wrong!). We must ensure that our toy problem captures this. What do you think about simple galaxies (2D Gaussians) with random orientations that have a long tailed intrinsic ellipticity distribution (closer to uniform[0:1] than truncatedRayleigh(width=0.25)), and perhaps making the ellipticity distribution vary with galaxy colour?
Regarding shear maps: if we are tackling cosmic shear, we need to think about mission definition. Can we split the investigation of Hierarchical Bayesian WL analysis into pieces? 1) investigate HB for ellipticity distribution joint with constant shear 2) investigate HB for shear map joint with power spectrum parameters
I am still unsure what to do about the "power spectrum" in 2) though, since it doesnt contain all the cosmological information we are really after anyway.
Regarding constant shear in 1), one could argue that to make a pixelated shear map you have to, at some point, estimate the shear in a pixel. The dumbest way to do that is to divide the sky onto a grid and then use teh galaxy shapes in each grid cell - so inferring a constant shear in a grid cell is not crazy if all we want to do is look at how much is to be gained by hierarchically inferring galaxy morphology.
Reply to this email directly or view it on GitHub: https://github.com/davidwhogg/WeakLensing/issues/1
@drphilmarshall sent this by email; let's do this!
The arguments you start to sketch, regarding hypothetical populations of highly ordered galaxies, are good for showing the reader our motivation - but in real life we work in the opposite regime, with high diversity between galaxy shapes. Most analysts' common sense is that in this case, and because of the diversity, simple averaging will be a close approximation to full-on hierarchical inference. Our aim is to investigate that assumption (not prove it wrong!). We must ensure that our toy problem captures this. What do you think about simple galaxies (2D Gaussians) with random orientations that have a long tailed intrinsic ellipticity distribution (closer to uniform[0:1] than truncatedRayleigh(width=0.25)), and perhaps making the ellipticity distribution vary with galaxy colour?
Regarding shear maps: if we are tackling cosmic shear, we need to think about mission definition. Can we split the investigation of Hierarchical Bayesian WL analysis into pieces? 1) investigate HB for ellipticity distribution joint with constant shear 2) investigate HB for shear map joint with power spectrum parameters
I am still unsure what to do about the "power spectrum" in 2) though, since it doesnt contain all the cosmological information we are really after anyway.
Regarding constant shear in 1), one could argue that to make a pixelated shear map you have to, at some point, estimate the shear in a pixel. The dumbest way to do that is to divide the sky onto a grid and then use teh galaxy shapes in each grid cell - so inferring a constant shear in a grid cell is not crazy if all we want to do is look at how much is to be gained by hierarchically inferring galaxy morphology.