We thank all reviewers for thoughtful feedback! We reply separately to each reviewer. Reviewer #1: We would like to point out some of the paper's main contributions, not fully recognized in the review. Another example is our algorithm for sampling DAGs conditionally on a root-partition (Sections 3.4 Accordingly, our main innovations are algorithmic. We would like to correct that our algorithm for sampling DAGs is not "classical" (cf.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Overview: The paper proposes a framework for enforcing structure in Bayesian models via structured prior selection based on the maximum entropy principle. Although the optimal prior may not be tractable, the authors developed an approximation method using submodule optimization. Contructing priors with structured variables is an important topic, so this method should be able to make good impact. Quality The paper is technically sound.

We focus on the case of i.i.d.

Humans can quickly learn new tasks from just a handful of examples by preserving rich representations of experience [1].

We give a tractable unbiased estimate of the log density using a "Russian roulette" estimator, and reduce the memory required

Bayesian decision theory outlines a rigorous framework for making optimal decisions based on maximizing expected utility over a model posterior. However, practitioners often do not have access to the full posterior and resort to approximate inference strategies.

They are themselves constructed from i.i.d. Gaussian processes, in analogy to the construction of Wishart or inverse Wishart random variables from i.i.d.

Quasi-Monte Carlo (QMC) is an essential tool for integral approximation, Bayesian inference, and sampling for simulation in science, etc.