Review Reports
- Ameer Musa Imran Alhseeni1 and
- Hossein Bevrani1,2,*
Reviewer 1: Anonymous Reviewer 2: Anonymous Reviewer 3: Anonymous
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsSee my attached file
Comments for author File: 
Comments.pdf
Author Response
Dear reviewer, thank you for your insightful review, which has significantly improved our manuscript. Our responses are in the attached file, and corrections are marked in red in the revised manuscript.
Author Response File: Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for Authors1) Please correct a typo on P.2, l2 up: perhaps, you mean $\sum \frac{k^y}{k!}$. 2) P.4, l.7 up: Do you mean $D_{KL}(P||Q)$ or $D_{KL}(Q||P)$? How to justify your choice? 3) P.4, L.14 down: what is $H(x)$- strange notation for a distribution. In general, the presentation on p.4 is not readable and notations are not properly introduced. Say, $X$ is a vector with mean $A$ but $E[X^TMu]$ does not depend on $A$. Please carefully introduce all notations ($n, p \ldots$) and correct typos.
Author Response
Dear reviewer, thank you for your insightful review, which has significantly improved our manuscript. Our responses are in the attached file, and corrections are marked in red in the revised manuscript.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsStrengths
- This research shows why an overdispersed alternative is needed.
- The Bayesian BRM with prior is useful.
- Good simulations.
- Simulations generally favor the G-prior
- The application shows BRM outperforming Poisson on fit criteria
Needs attention
- When introducing the G-prior, credit the original source (Zellner) and briefly say why your construction is appropriate for BRM.
- Specify Metropolis–Hastings tuning: proposal covariance choice, adaptation (if any), and target acceptance range.
- Include at least a Negative Binomial baseline in simulations and the application; if zeros matter, consider ZINB/zero-inflated Bell in an appendix.
- Fix minor typos
- Keep conclusions scoped to the evidence: “BRM > Poisson here; G-prior > diffuse normal in most settings tested.” Avoid implying superiority over NB without results.
Author Response
Dear reviewer, thank you for your insightful review, which has significantly improved our manuscript. Our responses are in the attached file, and corrections are marked in red in the revised manuscript.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsNo other comments
Author Response
Thank you for your review; your previous comments and corrections significantly improved our paper.
Reviewer 2 Report
Comments and Suggestions for Authors1) P.3: still wrong $B_y=e^{-1}\sum\limits_{k=0}^{\infty}\frac{k^y}{k!}$ 2) The set up is wrong: the authors consider the data $D=\{(y_i,X_i)\}$, and the formula (1) should define the conditional distribution $f(y\vert X)$ because $\theta=W_0(e^{X^T\beta})$. 3) p.4: `$\mu(X_i)=h^{-1}(X_i^T\beta)$'. What is $h$? If this is PDF of $H$, it makes no sense, ,etc.
Author Response
Thank you for your review; your comments and corrections significantly improved our paper.
Please see the attachment.
Author Response File: Author Response.pdf