Posterior Consistency in the Binomial Model with Unknown Parameters: A Numerical Study
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) . There, posterior contraction for n is proven in the problematic parameter regime where \(n\rightarrow \infty \) and \(p\rightarrow 0\) 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.
KeywordsBayesian estimation Binomial distribution Discrete parameter Posterior contraction Simulation study
Support of the DFG RTG 2088 (B4) and DFG CRC 755 (A6) is gratefully acknowledged.
- 11.Schneider, L.F., Schmidt-Hieber, J., Staudt, T., Krajina, A., Aspelmeier, T., Munk, A.: Posterior consistency for \(n\) in the binomial \((n,p)\) problem with both parameters unknown - with applications to quantitative nanoscopy. arXiv:1809.02443 (2018)