I have one question about the purpose of this paper: Is it to advocate ABC(Approximate Bayesian Computation) algorithm, or is it to analyze Sculptor dataset? If advertising ABC algorithm is more important, I think Section 4 should also contain baseline comparison algorithm, so that the reader can feel like ABC algorithm is beating other methods. For both Section 4.1 and Section 4.2, I would split one paragraph to two, where first paragraph describes experiments setting, and the second paragrpah describes its numerical result. In this way, skimming reader will not miss your result. Figure 6 I will use \subflot in subfig package, with which you can give label to each subplot. And I would say "(a)" instead of "left panel", and "(b)" instead of "right panel." I would use present tone "is" rather than past tone "was". Section 4.1. "Using the selected distance metric we run our ABC algorithm using the simplified density model described in the previous section the same simulated dataset with known parameter values as our "observed" data." -> "Using the selected distance metric in Section 3.1 and the simplified density model in Section 3.5, we run our ABC algorithm on the same simulated data set as our "observed data" with known parameter values": I didn't read Section 3(and some skimming reader will do the same), so I have no idea where the selected distance metric is coming from. By giving pointer to the previous section, it will help reader to understand. Also, it is better to give exact section rather than saying "previous section". "This allowed us" -> "This allows us" I will start a new paragraph from 3rd sentence, so that the first paragraph described the experiments setting, and the second paragraph describes numerical result. "The results are shown in the right panel of Figure 6. We can see that the posterior" -> "The results in Figure 6(b) shows that the posterior": By using \subflot, you can give label for each subfigure in large figure. I think it is better to refer as "Figure 6(b)" rather than "the right panel of Figure 6". "with increasing accuracy": Do you have measures for accuracy? If so, I will add those quantitative results. "somewhat lower than that of the true posterior this is not surprising" -> "lower than that of the true posterior, this is expected": "somewhat" and "surprising" sounds a little bit informal to me. Also, rather than saying that "posterior is only approximate", I would give some explanation about why approximate posterior tends to deteriorate peaks, not making peaks higher. (if it is possible) "would result in an improved approximation however, the additional computation time would be considerable and thus was not implemented" -> "would improve the approximation, however, is not implemented due to huge computation time" "with the difference being that they are somewhat wider" -> "with wider width" "Thus, we can expect that any credible intervals generated using our ABC posteriors would contain more values and an equivalent credible interval using the unknown true posterior.": I didn't really get this sentence. What do you mean by equivalent credible interval? Is credible intervals generated from ABC contains that eqvalent credible interval? Figure 7 I think this figure would be more effective if you overlay the previously estimated values of E_{c} and visually show that it lies outside credible interval. Section 4.2. "full galaxy simulation model" -> "full galaxy simulation model in Section 3.4" "These populations contain only 93 and 294 stars respectively so as we expect the posterior distributions are" -> "These populations contain only 93 and 294 stars, respectively, the posterior distributions are expected to be" I will start a new paragraph from 4th sentence, so that the first paragraph described the experiments setting, and the second paragraph describes numerical result. What do "previous estimates" / "the previously estimated value" mean? I think phrase like "we find that" is unnecessary. "In the case of the metal-poor population the posterior density" -> "In the case of the metal-poor population, the posterior density" "our distance functions as shown in Figure 5 that" -> "our distance functions, as shown in Figure 5, that": comma makes readers easier to break the sentence. Conclusion 1st paragraph "For the single parameter we estimated our results are inconsistent with those reported previously [4].": What does "For single parameter" mean? Does it mean a credible interval for individual parameter? I would write as "Our resulting credible intervals for individual parameters are inconsistent with those reported previously in [4]." "It is possible that if credible intervals were calculated for all parameters simultaneously that our joint intervals would not be inconsistent with the previously reported values.": I think this sentence is also somewhat overcomplicated. I would write as "If credible intervals were calculated for all parameters simultaneously, our joint intervals possibly would have been consistent with the previously reported values.". Also, do you have any reason to think that simultaneously calculated credible intervals will give consistent result? I would write more reasoning for this. I think I would make a new paragraph from 5th sentence(The simplest ~), about arguing that aBC algorithm is extracting more information. I will start the paragraph with "Our ABC algorithm is able to extract more information out of the data.". And explain in which sense method in [4] is losing the information, and how our ABC algorithm is keeping track of it / or extracting other information that is not in [4]. 2nd paragraph "Modeling both populations simultaneously as well as capturing other random would allow for greater power when estimating parameter values that affect both metal-rich and metal-poor populations as well as providing a more accurate model of the data generating process.": I think this sentence is too long and there are two "as well as" in the sentence, so it is a bit confusing to me. Also, what does "random" mean? I would write as "Modeling both populations simultaneously as well as capturing other features would allow for greater power when estimating parameter values that affect both metal-rich and metal-poor populations. Such model would be more accurate as the data generating process."