Thanks for the post on our paper!

We believe that this is a genuinely new and promising way forward in the shape measurement problem, and that by using a technique such as

*lens*fit the concern that shear bias may limit future weak lensing surveys could be eliminated.

For more information please visit

http://www.physics.ox.ac.uk/lensfit
on which there will soon be publically available code to download.

We

*do not* expect that the results presented will turn out to be incorrect. We have extensively tested the

*lens*fit pipeline and found it to be robust and accurate.

To answers your specific points:

1)

*lens*fit can measure the shear across any image in the same way as any other shape measurement method. The shear can be estimated on a galaxy-by-galaxy basis from the sensitivity weighted <

e>. So that in exactly the same way as every other shape measurement method one could choose apertures, measure shear in each aperture and vary the scale etc.

Furthermore since the entire posterior in ellipticity is determined the probability of shear

p(

g) could be fully and directly estimated by convolving the ellipticity distribution from each galaxy.

2) Yes we could have used 'hyper-priors' on the functional fit the prior, but in the case the the intrinsic ellipticity distribution is entirely unknown the only reasonable prior is a flat one, which is what we have implicitly assumed in the analysis presented in this paper.

Also, the shape of the ellipticity distribution is extremely well constrained by a large sample (i.e. the hyper-likelihoods for the parameters describing the prior are extremely sharply peaked) so we don't expect that this marginalisation would make much difference.

3) This an important point which we wish to clarify. The method

*does not * depend on a training set. The prior can be derived from the

*data itself*. As such it can be used on any data set. The only case in which this would break down is for *extremely* small data sets (of order a few hundred galaxies) e.g. snapshots of clusters, in this case the prior could be estimated from an external data set.

A medium-deep survey would be of use if the main survey was not complete to a certain magnitude say (though this is unlikely for future weak lensing experiments). In this case the deeper and more complete survey could be used to correct estimate the prior as a function of magnitude. Which could then be used for the wider survey.

In this process we are estimating the prior distribution of ellipticity, not the prior distribution of the shear. Over any one survey the shear is expected to average to zero (apart from in particular regions such as near a galaxy cluster).

If one then uses the ellipticities in some way to measure a shear statistic (mean shear, shear variance, shear correlation function, shear power spectrum, map statistic) then one could/should apply priors on gamma at that point, but

*lens*fit is a step removed from that stage of analysis.

4) There is a number of ways that there is an advantage in using the individual galaxy posterior likelihoods. Firstly any "bad" likelihood surfaces from individual galaxies could be identified and not used in the ensemble. Secondly in the case of multiple exposures the likelihood from the same galaxy from each exposure should be able to be combined in an optimal way.

When using the individual posterior the equation mentioned could be trivially computed, but the expression quoted for <

e> isn't what one would like to calculate. We could calculate the probability distribution in shear

p(

g) from the convolution of individual posterior probability distributions if we wished. But in the most straightforward analysis, if we don't wish to know the distribution of

g but just the mean, we can calculate the expectation value <

e>, computationally efficiently, because the expectation value of a sum is a sum of the expectations values.

5) We have a number of points on this issue. Firstly in STEP2 the zero-shear images were known. To quote the README given to the original STEP2 participants:

'In each case, image #00 contains zero shear, and can be used if your shear measurement method requires an ensemble galaxy population without it.'

So for STEP2 the results are fair an accurate.

For STEP1 we did use this information however (a) the majority of other authors didn't use a prior or ensemble average so that information was irrelevant for them (

b) for our method in particular the fact that the step shear is constant over the images is actually more difficult than in real data. This is because the constant high shear values might lead to an additional slight bias in the ellipticity prior (i.e. not being centered on zero) which would not exist in real data (where the shear varies on small scales). This is why we chose not to use the sheared images when estimating the ellipticity distribution prior.

Cheers

Tom Kitching