Bayesian Estimation of Neyman–Scott Rectangular Pulse Model Parameters in Comparison with Other Parameter Estimation Methods
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsPlease see the attached file
Comments for author File: 
Comments.pdf
Author Response
We appreciate your insightful and constructive comments on our paper. As a result, we were able to incorporate changes to reflect most of the suggestions provided by the reviewers. Please check the attached response.
Author Response File: Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsComments on “Bayesian estimation of Neyman-Scott Rectangular Pulse Model parameters in comparison with other parameter estimation methods ”
General comments:
This study use Neyman-Scott Rectangular Pulse model to analyze Seoul's hourly rainfall data during summer months and evaluate the method of moment estimation and the method of maximum likelihood estimation using different optimization algorithms with different initial values. The best accuracy of the estimates produced by different optimization methods is DEoptim.
Specific comments:
1. Detailed explanation of data. The article only states that precipitation data from Seoul was used, but the source of the data and how it was processed are not explained. Only mentioning summer precipitation in the abstract.
2. Why choose Seoul to validate this model? Or is there anything special about this place?
3. The introduction is very vague. The conclusion is directly stated in the introduction (line 69).
4. What is the purpose of this paper's research? I don't see that in the introduction.
5. The lines of Deoptim and dfp are not clearly shown in the figure.
6. The names of each model in the figure should be consistent with the paper, especially in case.（dfp and DFP）.
7. Where is figure 4 for line 333?
8. The author should present the advantages and disadvantages of these patterns in a more intuitive way, such as tables.
9. Line103-107 refenrence?
10. The section of Discussion is too few.
Comments on the Quality of English Languageminor revise needed.
Author Response
We appreciate your insightful and constructive comments on our paper. As a result, we were able to incorporate changes to reflect most of the suggestions provided by the reviewers. Please check the attached response.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsThe Neyman-Scott Rectangular Pulse is a stochastic model for rainfall that involves five parameters. In this study, authors examined how the initial values and optimisation approaches affect the estimate of these parameters in the Neyman-Scott Rectangular Pulse model. They employed both the method of moments and the method of maximum likelihood for parameter estimation. The paper reads well and can be accepted after major revisions:
1. Section Abstract: Line 14-59: Results and future works are missing in the abstract. It is recommended to revise the abstract by mentioning the quantitative percentages of the improvement. For example, authors mentioned sensitivity to initial values in line 18. Can you please elaborate how sensitive?
2. Section-Introduction: Authors only mentioned 9 citations which is not adequate for the introduction part. See line 54. Not many literature reviews are done in the introduction section. It will be highly desirable to read more literature and work out from there so that a clear picture can be drawn.
3. Section-Methods: In methods, authors described the model and it will be helpful to mention the limitations of models that have been used in this study.
4. Tables: A large number of tables (see up to table -9) are presented and few of them can go to the appendix section. The caption requires elaboration as it is not detailed.
5. Figures: Figure caption needs to be revised and elaborate as these are not explained in details.
6. Section-Discussion: In the discussion section, no study is compared. It is recommended to revise the discussion section by comparing with others relevant studies.
7. Section-Conclusion: Conclusion can be drawn by highlighting the findings which are currently missing.
8. Section-References: References are appropriate but can be added more when the literature reviews are done in the introduction section.
Comments on the Quality of English LanguageMinor editing is required.
Author Response
We appreciate your insightful and constructive comments on our paper. As a result, we were able to incorporate changes to reflect most of the suggestions provided by the reviewers. Please check the attached response.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsComments on “Bayesian estimation of Neyman-Scott Rectangular Pulse Model parameters in comparison with other parameter estimation methods ”
General comments:
The abstract provides a general overview of the application and rough results of the NSRP model. It is necessary to provide a detailed introduction to the main conclusions of this article, as well as the advantages or improvements of the model?
Specific comments:
L.76 The sentence ‘we adopted the MCMC method specifically slice sampling within the Gibbs sampler’ what is ‘MCMC’?
L. 157 Lee et al., Kim and Kim, and Mullen [11-13] constructed the likelihood function from the. two Kim is confused.
In section 3, Result analyze is not detailed. Foe example, ‘The results. in Table 2 and 4A2 show that both initial values 308 and optimization methods have an impact on NSRP parameter estimates.’,’ L.345 The results are given in Table 53 and Table 6A3.’ What’s means? Which method is better?
The conclusion is too simplistic.
Comments on the Quality of English LanguageMinor editing of English language required.
Author Response
Comments: The abstract provides a general overview of the application and rough results of the NSRP model. It is necessary to provide a detailed introduction to the main conclusions of this article, as well as the advantages or improvements of the model
Response: The abstract has been improved and reduced to a maximum of 200 words per journal guidelines, including the following points.
Background
1) Definition of NSRP
2) Problem with the estimation of NSRP parameters using frequentist methods and the impact of these methods
Method
3) The proposed solution and its advantages
Result and Conclusion
4) The result of the comparison between frequentist Parameter estimation methods and the proposed Bayesian estimation method and the conclusion
Below is the improved abstract
Neyman-Scott Rectangular Pulse is a stochastic rainfall model with five parameters. The impacts of initial values and optimization methods on the parameter estimation of the Neyman-Scott Rectangular Pulse model were investigated using both method of moments and method of maximum likelihood. The estimates using the method of moments are influenced by the optimization method and are sensitive to the initial values and the aggregation scale of the data. Thus, by using frequentist estimation methods, we cannot guarantee the unique values as estimates. The aim of this study is to find more reliable unique values as estimates using a Bayesian approach. In this approach, parameters are estimated from the posterior distribution, and model performance is assessed by comparing observed values with fitted values. The slice sampling within Gibbs sampler algorithm demonstrates superior convergence and model fitting, yielding unique estimates for the model parameters. The main conclusion of this study is that Bayesian estimation methods outperform other estimation methods in terms of providing reliable and stable estimates which improve rainfall generation accuracy.
Specific comments
- 76 The sentence ‘ We adopted the MCMC method specifically slice sampling within Gibbs sampler” What is “ MCMC”
Response: MCMC stands for Markov Chain Monte Carlo. It's a powerful algorithm for drawing samples from a probability distribution, especially when complex. This is particularly useful in Bayesian statistics for estimating posterior distributions. it is explained first on L259
- L157 Lee et al. Kim and Kim and Mullen [11-13] constructed the likelihood function from two kim is confused
Response: Reference no 12 has two authors, Yongku Kim, and Dal Ho Kim, they share the common surname, Kim
- In section 3, Result analyze is not detailed. For example. The results in Table 2, and A2 show that both initial values 308 and optimization methods have an impact on NSRP parameter estimates’, L345 the results are given in Table 53 and Table 6A3 what’s means? Which method is better?
Response: We have improved and clarified these sentences in the revised manuscript. As follows
Line 307 in the revised manuscript: The results in Table 2 show the NSRP parameter estimates using the range of initial values in Table 1. The results in Table A2 show the NSRP parameter estimates using the range of initial values in Table A1. From Tables 2 and A2, we can see that both the initial values and optimization methods have an impact on NSRP parameter estimates
L 347 in the revised manuscript: the results presented in Table 3 show the NSRP MLE parameter estimates using the range of initial values from Table 1. Additionally, the results in Table A3 display the NSRP MLE parameter estimates using the initial values from Table A1. Both Table 3 and Table A3 indicate that the maximum likelihood estimation (MLE) is sensitive to initial values and optimization method
The main target of our research was to show that initial values and optimization methods influence parameter estimates. Though it was not the main target of this study. The first paragraph of the discussion section compare the methods and ordered them in terms of providing good estimates that are close to the true parameter.
For the general comparison between the frequentist estimation methods and the Bayesian estimation method. The Bayesian outperforms the frequentist estimation methods in terms of producing unique estimates.
- The conclusion is too simplistic
Response: True; although most of the information is presented in the discussion part, we have improved the conclusion section. As follows
In conclusion, the results of this study unequivocally establish the efficacy of the Bayesian estimation method in producing NSRP parameter estimates that are both distinctive and highly reliable. Significantly, our findings indicate that this method shows great promise in enhancing the precision and dependability of NSRP parameter estimates, which is crucial for engineering applications reliant on accurate rainfall data for design and planning purposes. The rainfall statistics derived from the estimates closely correspond with the actual rainfall in Seoul, affirming the suitability of this method for NSRP parameter estimation. Further investigation and validation of this approach within engineering contexts have the potential to drive substantial progress in rainfall estimation and its impact on engineering design and infrastructure planning.
Author Response File: 
Author Response.docx
