Posterior consistency in the binomial model with unknown parameters: A numerical study

Laura Fee Nern, Thomas Staudt, Axel Munk

Abstract: Estimating the parameters from k independent Bin(n, p) random variables, when both parameters n and p are unknown, is relevant to a variety of applications. It is particularly difficult if n is large and p is small. Over the past decades, several articles have proposed Bayesian approaches to estimate n in this setting, but asymptotic results could only be established recently in Schneider et al. (arXiv:1809.02443, 2018) [11]. There, posterior contraction for n is proven in the problematic parameter regime where n→∞ and p→0 at certain rates. In this article, we study numerically how far the theoretical upper bound on n can be relaxed in simulations without losing posterior consistency.