Review Reports - The Nature of Mathematical Models

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Please see the attachment.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Dear authors,

The paper addresses an interesting and non-trivial topic. Formalising the connection between the world of models and the world of data is an important methodological task. The authors should add an illustrative example. For example, the article doi: 10.1134/S1061934825701527.

Check please list of properties (p.7, lines 250-260), it looks like unnecessary and disconnected part of manuscript.

Sincerely,

The Reviewer

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript title is “The nature of mathematical models”, referring to general models, and then in the abstract the author mentions the model as an operator in the Hilbert space of finite-variance random variables, random variables correspond to stochastic models, these are a very specific type of model.
In the introduction, the author begins by presenting general concepts of models but later goes on to define the concept of probability, as well as other ideas related to the field of probability, which again is not a general area of mathematical modeling.
The article comes from very general discussions of mathematical modeling and highly specialized topics like Hilbert spaces, probability theory, and differential geometry, without maintaining a clear and consistent focus.
The paper introduces extensive formalism, like Hilbert spaces, random variables, manifolds, tangent spaces, etc. that may not be necessary for addressing the core ideas of basic mathematical modeling.
Also, many of the concepts are classical and well-established, so the paper contribution is not clear.
The paper objective is to formalize the relationship between abstract modeling and statistical estimation, but this is not clearly developed into a concrete result.
Most of the paper is devoted to formal definitions and notation, while discussion and interpretation are relatively limited.
Section 2.1.2 described the Jacobian matrix, while the previous sections mentioned random variables, in discrete time these variables might be derivable, in continuous-time these are discontinuous and cannot be derived, the author needs to specify if he is either modeling in continuous or discrete time.