A Bayesian Nonparametric Learning Approach to Ensemble Models Using the Proper Bayesian Bootstrap

Round 1

Reviewer 1 Report

The main aim of this paper is to employ Proper Bayesian bootstrap (PBb) method in the data generative process introducing an ensemble approach based on decision tree models.
The element of novelty of this paper is to introduce Proper Bayesian Boostrap for classification and regression ensemble trees models and compare the results obtained on simulated and real datasets with respect to classical bootstrap approaches available in the literature as Efron’s and Rubin’s bootstraps. More precisely, PBb is used to sample the posterior distribution over trees, introducing prior distributions on the covariates and the target variable.

The paper is generally well-written and easy to follow. The results appear novel.

No noticeable typos were found, except maybe for "Proper Bayesian _Boostrap_", "techinques", others possibly, please check.

In section 2, please number the standalone equations.

Please make sure all notation is properly introduced, e.g.
- the "L" operator in (1),
- the \mathds{1}_n in the multinomial distribution introduced in the paragraph before the first standalone eqn. in "Effron's bootstrap" section,
- the \mathds{I}_{[X_i \leqq x]} in the definition of F^*(x) of the standalone equation in Section 3,
- etc.

For easy referencing, all subsections must be numbered also.

The "model stability" concept could be explained better. And you could also better emphasize how is this defined and measured in this work.

Author Response

See the attached file

Author Response File: Author Response.pdf

Reviewer 2 Report

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Comments for author File: Comments.pdf

Author Response

see the attached file.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

No further comments