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 \(n\rightarrow \infty \) 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.
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Support of the DFG RTG 2088 (B4) and DFG CRC 755 (A6) is gratefully acknowledged.
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Schneider, L.F., Staudt, T., Munk, A. (2019). Posterior Consistency in the Binomial Model with Unknown Parameters: A Numerical Study. In: Argiento, R., Durante, D., Wade, S. (eds) Bayesian Statistics and New Generations. BAYSM 2018. Springer Proceedings in Mathematics & Statistics, vol 296. Springer, Cham. https://doi.org/10.1007/978-3-030-30611-3_4
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DOI: https://doi.org/10.1007/978-3-030-30611-3_4
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