Robust Statistical Approaches for Stratified Data of Municipal Solid Waste Composition: A Case Study of the Czech Republic

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This article proposes a statistical framework based on stratified sampling for reliable estimation and data aggregation of the composition of municipal solid waste (MMW) under small sample conditions, solving the bias problem caused by insufficient sample size in traditional methods.

But before accepting, the following issues should be considered.

1、The mathematical symbols in Appendix A need to be uniformly explained (such as K_n physical meanings), and it is recommended to add a brief table to summarize variable definitions.

2、The division criteria for the 10 clusters in Figure 3, such as population density and economic indicators, should be supplemented to enhance the credibility of the hierarchical logic.And it is mentioned on this page that seasons affect the composition of waste (Page 9), but the results of seasonal data analysis are not shown. It is recommended to supplement.

3、It is estimated that 43 representative points are needed at the national level (Page 11), but the cost feasibility has not been analyzed. It is suggested to discuss a compromise solution.

4、In the conclusion section, there is a significant difference in the composition of Czech MMW (28.4% biological waste) compared to Western European countries, and the impact of this difference on the generalization of the method needs to be discussed.

5、In addition, attention should be paid to the standardization of the charts and tables in the article. The titles should be placed in the center, and the tables should adopt a standardized three line table format, for example, Table 2 and Table 3.

6、Partial long sentences can be split (such as Abstract) to avoid redundant expressions (such as repeated feedback mechanism descriptions in Page 3).

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

1. Vocabulary and Terminology: Please conduct a thorough proof-reading of the manuscript to eliminate spelling errors—for example, the section title “1.1 Research gap and challanges” should read “challenges.” In addition, ensure that every technical term or acronym is defined upon its first appearance: e.g., the acronym “SWA-Tool” is introduced at line 56 but not explained as “solid waste analysis” until line 107. Addressing such issues will enhance the paper’s precision and overall scholarly quality.
2. Coherence of the Introduction: The logical flow of the introduction is currently weak. The opening statement “Changing the current waste-management (WM) system and switching to recycling is a demanding and costly process” does not connect seamlessly to the subsequent claim that “to ensure the sustainability of the entire WM and reduce the amount of emissions, modelling scenarios and accurate estimates of waste composition are needed.” Please revise this section to establish a clear, step-by-step rationale that links the practical challenges of WM reform to the necessity for scenario modelling and compositional forecasting. Strengthening these connections will improve the clarity and persuasiveness of the introductory argument.
3. Clarity of Research Objectives and Novelty in the Introduction: The explanation of the study’s aims and novelty is presently disjointed. Line 52 states that “the goal of the presented paper is analysis of the latest methodology for the statistical evaluation of waste composition, the identification of its limits, and design improvements to get a comprehensive tool,” signaling the manuscript’s central focus. Yet a detailed treatment of these contributions does not appear until Section 1.2 “Novelty and main contribution.” This temporal gap disrupts the narrative and risks confusing readers. I recommend reorganizing the introduction so that the research objectives and principal innovations follow immediately after the context and identified research gap. Presenting these elements together will improve coherence and ensure that readers clearly grasp the manuscript’s contributions from the outset.
4. Representativeness and Reproducibility of the Sampling Protocol: The seven-step sampling framework remains non-reproducible because key methodological details are omitted. Please disclose the variables, distance metric and algorithm used for cluster analysis, quantify the “best-representative” selection rule, and detail the intra-city stratification and container randomization procedure. Furthermore, because Section 3.1 “Waste analysis information” reports a total sample mass of only 19.4 t of MMW, the discussion should explicitly assess how geographic heterogeneity and socio-economic stratification might bias the observed composition and identify the boundary conditions.
5. Conclusion: The conclusion claims that the proposed framework will " will reduce the cost of analysis". However, the main text lacks any quantitative cost-benefit analysis or comparative case studies to substantiate this assertion. It is recommended to add some references to prove this point.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This study presents a statistical approach based on territorial stratification, which aggregates data from individual waste container analyses to higher geographic units. This research is meaningful, but there are some problems in the manuscript that need to be improved.

• The abstract needs to be revised. For example, clarify the data source, etc.
• The review covers prior studies but could better highlight gaps and how this work advances the field. A more critical analysis of existing limitations and a clearer articulation of this study’s novel contributions would strengthen the theoretical foundation.
• The paper provides a detailed description of the stratified statistical approach, but some mathematical models are complex and may hinder readability. It would be beneficial to include more practical examples or simplified explanations of key formulas to improve comprehension.
• The analysis is based on a relatively small sample (19.4 tons of waste), which may limit the generalizability of the findings. A discussion on how sample size affects statistical power and whether a priori sample size calculations were performed would strengthen the methodology.
• The division of the Czech Republic into 10 clusters is mentioned, but the exact stratification parameters (e.g., population density, economic factors) are not thoroughly explained. A more detailed rationale for these criteria would improve methodological rigor.
• Three interval estimation approaches are proposed, but their comparative advantages and limitations are not sufficiently explored. A simulation-based comparison or real-world validation would help demonstrate the superiority or suitability of these methods.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

Authors of this manuscript have adequately addressed all comments and suggestions made by reviewers and editors; I would like to congratulate them for the effort. This version of the manuscript is significantly improved; therefore, I recommend publishing the manuscript as it is.
Sincerely,