. We thank Reviewer # 1 for pointing out this interesting work. Both our

We thank all reviewers for taking the time to provide detailed feedback and valuable suggestions for our work. However, their PDFs' exact expressions are in fact different. Alternatively, one can also use the No U-Turn Sampler (NUTS) implemented in Stan. As shown in equation (5) of the main text, BNE's mean function consists of the In the experiment, BNE is by construction more expressive than BAE. Figures 4-5 suggest that the former is true, but not the latter.