Posterior Consistency in the Binomial (n,p) Model with Unknown n and p: A Numerical Study
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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. 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.
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