Posterior analysis of n in the binomial (n,p) problem with both parameters unknown—with applications to quantitative nanoscopy
二项模型中参数均未知时总体规模的后验分析及定量纳米成像应用
Estimation of the population size n from k i.i.d. binomial observations with unknown success probability p is relevant to a multitude of applications and has a long history. Without additional prior information this is a notoriously difficult task when p becomes small, and the Bayesian approach becomes particularly useful. For a large class of priors, we establish posterior contraction and a Bernstein-von Mises type theorem in a setting where p→0 and n→∞ as k→∞. Furthermore,…