[0802.1528] Bayesian Galaxy Shape Measurement for Weak Lens
Posted: February 15 2008
Lensfit seems to be an exciting methodology breakthrough for weak lensing. Even if the improvements on the STEP simulations reported here turn out to be incorrect, I think this Bayesian approach opens the door to a more robust reporting of errors in WL methods.
That being said, I do have some questions/comments that I hope the community (or the authors) could shed some light on.
1.) Given a catalog of galaxies, this method seems to be able to fit only a constant shear. With the use of expectation values to fit g, how would this method be expanded to measure a varying shear field over an image?
2.) Fitting the prior from the data seems reasonable. I think in the stats world this is known as a 'hierarchical model.' However, the A-D variables in the paper's prior would need some defined 'hyper prior' to be fully Bayesian; hyper priors tend to be simple distributions. Since the priors are irrelevant to the measurement, the prior parameters need to be marginalized. That doesn't seem to be the case in this paper.
3.) The method seems to depend on a training sample to extract the prior for the shape measurement (as opposed to a hierarchical model). If this method really does need a training set, can it not be applied to current datasets?
The paper also mentions that future surveys would have a 'medium depth' auxiliary survey outside the main cosmic shear survey to allow for this training. How would this work? Don't we expect cosmic shear in this training sample? Also, wouldn't galaxy shape evolution, such as the change in the fraction of barred spirals, be neglected in a shallower sample?
4.) Is there an advantage to working with the expectations of the individual galaxy posterior probability functions? A more Bayesian approach is to carry along the posteriors. Then <e> = \int e \Pi P(e|y_i) de, and g would be fit as an explicit parameter in the statistical model.
5.) Is comparing this method's m & c values from the STEP papers a fair comparison to other methods reported in STEP1 & STEP2? The authors used extra information (the identity of unsheared images) that was unavailable during the STEP competitions. If the prior was inferred from the data as described above in point (2), then I would expect the results to be degraded to some degree, or at the very least have larger error bars.
Good paper, and I look forward to any responses.
Cheers,
Douglas Applegate
That being said, I do have some questions/comments that I hope the community (or the authors) could shed some light on.
1.) Given a catalog of galaxies, this method seems to be able to fit only a constant shear. With the use of expectation values to fit g, how would this method be expanded to measure a varying shear field over an image?
2.) Fitting the prior from the data seems reasonable. I think in the stats world this is known as a 'hierarchical model.' However, the A-D variables in the paper's prior would need some defined 'hyper prior' to be fully Bayesian; hyper priors tend to be simple distributions. Since the priors are irrelevant to the measurement, the prior parameters need to be marginalized. That doesn't seem to be the case in this paper.
3.) The method seems to depend on a training sample to extract the prior for the shape measurement (as opposed to a hierarchical model). If this method really does need a training set, can it not be applied to current datasets?
The paper also mentions that future surveys would have a 'medium depth' auxiliary survey outside the main cosmic shear survey to allow for this training. How would this work? Don't we expect cosmic shear in this training sample? Also, wouldn't galaxy shape evolution, such as the change in the fraction of barred spirals, be neglected in a shallower sample?
4.) Is there an advantage to working with the expectations of the individual galaxy posterior probability functions? A more Bayesian approach is to carry along the posteriors. Then <e> = \int e \Pi P(e|y_i) de, and g would be fit as an explicit parameter in the statistical model.
5.) Is comparing this method's m & c values from the STEP papers a fair comparison to other methods reported in STEP1 & STEP2? The authors used extra information (the identity of unsheared images) that was unavailable during the STEP competitions. If the prior was inferred from the data as described above in point (2), then I would expect the results to be degraded to some degree, or at the very least have larger error bars.
Good paper, and I look forward to any responses.
Cheers,
Douglas Applegate