PONE-D-24-59633Optimal experimental design for partially observable pure birth processesPLOS ONE

Dear Dr. Skerritt,

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PLOS ONE

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Additional Editor Comments:

This paper presents a novel algorithm designed to identify optimal observation times by maximizing the Fisher information associated with the birth rate in a partially observable pure birth process involving nnn observations. In this context, "partially observable" signifies that, at each scheduled observation time, individuals in the process are independently observed with a fixed probability ppp, effectively modeling real-world challenges such as detection uncertainty or limited observational resources.

To address the computational complexity of this problem, the authors employ techniques from generating function theory, integrating symbolic and numerical computations to construct a recursive formulation for calculating the Fisher information. Although the recursion remains computationally intensive, it offers substantial improvements over previously existing methods, which proved to be computationally prohibitive even in the relatively simple cases. The paper demonstrates the efficacy of this approach through numerical experiments and provides a publicly accessible implementation.

I think this paper addresses an important problem in the design of experiments for partially observable stochastic processes. The authors introduce a novel approach by incorporating generating functions to compute and optimize the Fisher information, offering improvement over existing methods in terms of scalability and computational feasibility.

The manuscript has been evaluated by two reviewers—one recommending acceptance and the other suggesting minor revision. In light of these assessments, I recommend minor revision. The paper is methodologically sound and contributes meaningfully to the literature; however, I encourage the authors to address all comments and suggestions raised by both reviewers thoroughly and carefully to further strengthen the clarity and impact of their work.

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Reviewers' comments:

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Comments to the Author

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Reviewer #1: Yes

Reviewer #2: Yes

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

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Reviewer #1: Yes

Reviewer #2: Yes

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Reviewer #1: Yes

Reviewer #2: Yes

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5. Review Comments to the Author

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Reviewer #1: Title :Optimal experimental design for partially observable pure

birth processes .

After reviewing the research and its findings, I find that the study is well-conducted and its results are accurate and valid. Therefore, I recommend its acceptance in its current form.

Reviewer #2: This work addresses the optimal experimental design for partially observable pure birth processes (POPBPs), aiming to maximize the Fisher information with respect to the birth rate parameter. The authors introduce an innovative computational approach that leverages generating functions and symbolic computation to efficiently compute the Fisher information for these complex stochastic processes. This study is clearly relevant to researchers in stochastic modeling, applied probability, and statistical inference.

This work addresses the optimal experimental design for partially observable pure birth processes (POPBPs), aiming to maximize the Fisher information with respect to the birth rate parameter. The authors introduce an innovative computational approach that leverages generating functions and symbolic computation to efficiently compute the Fisher information for these complex stochastic processes. This study is clearly relevant to researchers in stochastic modeling, applied probability, and statistical inference.

The application of generating function techniques to optimize Fisher information in partially observable birth processes is novel and represents

a significant advancement over previous methods that were restricted to small values of $n$. The recursive formulation provides a practical computational tool, enabling computations for larger values of $n$ that were previously intractable. The theoretical derivations are well-structured, with clear formulations of generating functions, recurrence relations, and their implications for the likelihood and Fisher information.

The provision of a publicly available C++ implementation and GitHub repository further enhances the reproducibility and potential impact of the work.

In conclusion, this work is novel, interesting, and meaningful. Moreover, the presentation of this paper is clear and the proofs and computations appear to be correct. Therefore, I recommend that the paper be accepted for publication in $\textit{PLOS ONE}$.

However, the authors should carefully proofread the manuscript, as there are still some typographical and grammatical errors. For example:

\begin{enumerate}

\item The notation involving multiple indices (e.g., $\overline{y}_n$, $\overline{c}$, $q_{\overline{c}}$ ) may be overwhelming for readers unfamiliar with combinatorial generating functions. Consider adding a summary table of notation for reference;

\item Figure references (e.g., Fig. 1, Fig. 11) should be cross-checked to ensure correct linkage and appropriate caption placement;

\item Page 21, line 711: ``of of six days" $\longrightarrow$ ``of six days";

$\cdots$

\end{enumerate}

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Reviewer #1: No

Reviewer #2: No

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Submitted filename: Reports on PONE-D-24-59633.pdf

Optimal experimental design for partially observable pure birth processes

PONE-D-24-59633R1

Dear Dr. Skerritt,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

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Kind regards,

Hoda Bidkhori

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Thanks for addressing the comments.

Reviewers' comments: