Longitudinal Data Analysis Based on Bayesian Semiparametric Method

Round 1

Reviewer 1 Report

The authors mentioned their major contribution is  proposal of a semi-parametric autoregressive model with the Ornstein-Uhlenbeck process. The authors mentioned the connection between the autoregressive covariance matrix and Gaussian processes in the abstract and introduction. However, they did not explore it more in the main part of the paper or appendix. This part should be more elaborated. 

The authors can discuss more relevant papers and cite them in the introduction (i.e. Bayesian Nonparametric Longitudinal Data Analysis (Quintana, et al. 2016),  and An additive Gaussian process regression model for interpretable non-parametric analysis of longitudinal data (Cheng et al. 2019)) and compre with this work.

The captions and titles of figures contain minimum explanations (i.e. Figure 3, 4, 6, 7, 9, 12) such as the difference between orange and blue lines. The labels of the learned parameters do not match the equations. 

The authors could at least show the performance of their model on a real dataset.

The authors could make their code public otherwise there is nothing very significant about this paper.

In line 77, there is a typo which should be fixed: π(θ|x). On page 20, should the σs2  be an Inverse Gamma?

If the authors could make a figure containing the graphical model of this semi-parametric regression model, the figure makes it much easier for readers to understand the whole structure of the model and even compare it with the structure of previous works.

Some of the equations in section 7 (subsection 7.1) could be moved to the appendix potentially.

 

Author Response

see attached file

Author Response File: Author Response.pdf

Reviewer 2 Report

Apparently, I've got not the final text of the article, and the text editing is required

1) not all lines and formulas have numbers

2) Line 136) the text is inconsistent, since the values defined here that are not used above, etc.

Author Response

see attached file

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

 

 

1.  It is not clear to me to what extent this paper is different from "Bayesian Nonparametric Longitudinal Data Analysis" by Quintana et al.? Quintana et al mentioned "In this paper, we developed a generalization of many popular existing models for longitudinal data that results in a novel and somewhat general Toeplitz structure for the GP part of the model." The authors of this paper also claimed the same property "The SPAR model in this paper generalizes some existing models for longitudinal data analysis in the sense that it employs a new and more flexible circulatory correlation structure (called the Toeplitz structure)." What are the clear novelties in your paper compared to the aforementioned paper? 
2.  The parameters of the model have changed constantly through the paper and make it very difficult to follow the paper. There should be a table with the definition of each single parameter and they should not be changed through the paper. An example of confusing the reader with misuse of the parameter, in the first equation of page nine, the equation should be p(s_i|G). It has been modified in equation 15 which brings the question of why authors rewrite the same content with different notation in the next page? 
3. First equation in (9) should be y_i|beta,s_i,b_i,theta, sigma~F(theta, other params).
4. Figure 3 should be the first figure in this paper and it can be improved to make it easier for readers to understand the complexity of this model.
5. The bullet points in section 4 of page 7 can be improved in terms of their content (poorly written).
6. In section 3, the Gaussian process applied to `S` parameter (the authors mentioned earlier in the paper) while in the formula which is written in this section it is changed to `X` which is really confusing.
7. Figure 1 should be mentioned after equation Xt+1 = Xt +θ(μ−Xt)+εt+1  to make it easier for readers to follow the hyperparameters above the figure (Is this equation related to S or X )?
8.  I think there is no need to describe the stick breaking process. (line 134).
9. What is `m` in equation 38?
10. In figure 4, I suggest authors show the true value with a horizontal line to show their results converged... (It is not clear to which parameter of inverse Wishart model sigma_s^2 and sigma^2 posteriors have converged?)
11. Could the authors explain more the purpose of the energy graph (figure 6) and the plot can be improved since the labels are mixed and not explained well.
12. It is better if authors could provide the link to the real wind speed dataset in section 7.3 if it is a publicly available dataset.

Author Response

See attached file.

Author Response File: Author Response.pdf

Reviewer 2 Report

no more comments

Author Response

We thank Reviewer 2 for carefully reading our manuscript and recognize our contribution. Because of no further comments given, we did not prepare a point-by-point response report.

Round 3

Reviewer 1 Report

I appreciate that authors kindly take more time to address some of my comments and concerns. To make the paper much easier to follow, I have a few more comments which I hope it will help to improve the presentation of the paper :

1)The url links can move to footnotes in line 224, 231 (page 17).

2) Could authors explain why the multiple posterior sampling of DP which are not coinciding with each other in Figure 7 while in Figure 4 they all overlap? What is the reason for the difference?  

3) The authors maybe can keep Figure 4,5,6 in the main text and they could refer the readers to the appendix for the rest of figures and related text (Figure 7, 8,9,10,1,12, 13,14,15). If there are any significant differences between these four examples then it can be explained in the main part of the paper.

4) I am wondering which parameter of inverse gamma posterior distributions (i.e. the scale or  shape or mean  parameters of σs2 and σ2 ) are plotted in Figure 4,7? The captions should clarify this.

 

 

5) Figure 17 can be plotted in log scale  along with y axis because it is not clear that it really converges to zero.

6) All Figures related to the analysis of real dataset can be moved to appendix except on set of Figures (i.e. Figure 16,17,18).

 

Author Response

See attached response file

Author Response File: Author Response.pdf