Priyantha Wijayatunga’s contribution to the Discussion of ‘Martingale Posterior Distributions’ by Fong, Holmes, and Walker
讨论了参数估计中不确定性源于缺失观测，指出通过插补观测无法正确消除不确定性，因为插补估计与真实估计可能收敛到不同值。
Statistical uncertainty in (an estimate of) a parameter of a probability distribution is due to missing (unseen) observations (when it is estimated), as authors have noted. We can think that an estimate of the parameter has the maximal uncertainty when no observation is used for it, and no uncertainty when all possible observations are used for it. For example, in Bayesian sense, for a Bernoulli parameter, Beta distribution with parameter values = 1 and = 1 represents the full uncertainty. If observation counts are infinite, i.e., and are infinite, then there is no uncertainty. The uncertainty of the parameter estimate may be vanished when imputed or really observed data counts used for it are infinite, but the two estimates may converge to different values where the latter is the true value. But unfortunately we often do not have the chance to get it. So, it is not possible to eliminate the uncertainty correctly, i.e., while obtaining the true limiting value for the estimate, by imputing some observations given that some other observations are unknown.