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Posterior Consistency in the Binomial Model with Unknown Parameters: A Numerical Study

  • Laura Fee SchneiderEmail author
  • Thomas Staudt
  • Axel Munk
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 296)

Abstract

Estimating the parameters from k independent Bin(np) 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.

Keywords

Bayesian estimation Binomial distribution Discrete parameter Posterior contraction Simulation study 

Notes

Acknowledgements

Support of the DFG RTG 2088 (B4) and DFG CRC 755 (A6) is gratefully acknowledged.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Laura Fee Schneider
    • 1
    Email author
  • Thomas Staudt
    • 1
  • Axel Munk
    • 1
  1. 1.Institute for Mathematical Stochastics, University of GöttingenGöttingenGermany

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