Posterior analysis of n in the binomial (n,p) problem with both parameters unknown—with applications to quantitative nanoscopy

Anselm Johannes Schmidt-Hieber, Laura Schneider, Thomas Staudt, Andrea Krajina, Timo Aspelmeier, Axel Munk

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
38 Downloads (Pure)

Abstract

Estimation of the population size n from k i.i.d. binomial observations with unknown success probability p is relevant to a multitude of applications and has a long history. Without additional prior information this is a notoriously difficult task when p becomes small, and the Bayesian approach becomes particularly useful. For a large class of priors, we establish posterior contraction and a Bernstein-von Mises type theorem in a setting where p→0 and n→∞ as k→∞. Furthermore, we suggest a new class of Bayesian estimators for n and provide a comprehensive simulation study in which we investigate their performance. To showcase the advantages of a Bayesian approach on real data, we also benchmark our estimators in a novel application from super-resolution microscopy.
Original languageEnglish
Pages (from-to)3534-3558
Number of pages24
JournalAnnals of statistics
Volume49
Issue number6
DOIs
Publication statusPublished - 1 Dec 2021

Keywords

  • Bayesian estimataion
  • Bernstein-von Mises theorem
  • Beta-binomial likelihood
  • binomial distribution
  • Posterior contraction
  • Quantitative cell imaging
  • 22/2 OA procedure

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