We agree that including these baseline can be useful for the potential readers and

We thank all the reviewers for their time and valuable feedback. We didn't tune the kernel bandwidth but simply apply the widely used median trick [2]. The thinning factor is common in MCMC and has been used for decades. We will add sensitive analysis on that. The reference in L.100 should be referred to equation between L.80 and L.81 and we will fix it as well as the other Appendix A.4 should be Appendix C and Appendix A.5 should be Appendix C.1.