The Systematic Bias of Entropy Calculation in the Multi-Scale Entropy Algorithm

Round 1

Reviewer 1 Report

The paper discusses the fact that the MSE method contains a systematic bias coming from the coarse-graining of the data and proposes a correction to that bias. The paper is also equipped with an example.  Since the paper is clearly written and the main point of the paper is surely important, I suggest accepting the paper for publication.

Author Response

We thank the reviewer for the enthusiasm about our paper. We have gone through the English writing and corrected some writing erros.

Reviewer 2 Report

In this article, the authors consider the problem of multi-scale sample entropy (MSE), which calculates entropy through the sample entropy (SampEn) formula at each time scale. They MSE algorithm calculate the SampEn at different scales based on the same matching threshold, which introduces systematic bias to the calculation results. The purpose of this paper is to provide theoretical derivation for the systematic bias and to provide methods for correcting the bias.

I found the paper is interesting, and is of some interest, in theoretical point of view.

I think it is better to give some motivations about this problem and It will be helpful to give some simulations and real data application.

I recommend a minor revision for a possible publication. 

Author Response

We thank the reviewer for the enthusiasm about our paper.  

We have revised the manuscript to correct the English writing errors and provide more motivations. We can  provide real application example if more revision time will be allowed. Nevertheless, the described phenomenon and the correction method can be applied to any applications that MSE have and can be applied. In other words, the content of the paper is independent of applications.