David Draper and Erdong Guo's contribution to the discussion of ‘Martingale posterior distributions’, by Fong, Holmes and Walker
David Draper, Erdong Guo · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 2023
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.