David Draper and Erdong Guo's contribution to the discussion of ‘Martingale posterior distributions’, by Fong, Holmes and Walker
本文评论了 Fong 等人关于鞅后验分布的论文，指出其核心思想与 Fisher 一致性概念有百年渊源，并证明频率学派自助法样本与狄利克雷过程样本渐近等价，对高质量贝叶斯数据科学有实用价值。
We have two comments motivated by this interesting paper. The idea, introduced early in the paper, that ‘the object of interest is fully defined once all the observations have been viewed’ is almost exactly 100 years old: it was a cornerstone of the remarkable paper by Fisher (1922) and has been referred to for many decades as Fisher consistency. We are surprised that the authors did not make this connection. Theorem (Draper & Guo, 2023) Under the conditions detailed above, frequentist bootstrap samples of size n from (y1,…,yn) are asymptotically stochastically indistinguishable from stick-breaking samples of the same size from DP(n,F^n). We find empirically that the frequentist bootstrap approximation is good to excellent even for n as small as 25; this has useful implications for high-quality Bayesian data science.