A cautionary note on the discrete uniform prior for the binomial N

Ecology
William A Link

Abstract

Analysis of wildlife data frequently involves estimation of population size N based on binomial counts. Bayesian analysts often use a constant prior for N, the choice motivated by a desire to avoid an informative prior, and to let the data speak for themselves. For instance, data augmentation methods for model Mh posit a super-population of size M > N with individual detection probabilities z(i)p(i), with p(i) sampled from a parametric family of interest, and z(i) an indicator of membership in the target population; thus, N = Sigma(i)z(i). Treating z(i) as independent Bernoulli trials with success rate psi and assigning a uniform prior to psi is equivalent to assigning a discrete uniform prior for N on {0, 1,2,..., M}; by setting M large enough, analysts approximate the improper constant prior on the positive integers. In this paper, I demonstrate some paradoxical and plainly unacceptable features of the constant prior. These defects are not shared by the scale prior, which has been recommended for its good performance as measured by frequentist criteria. I show how the scale prior can be approximated in program OpenBUGS, including data augmentation applications for individual covariates.

References

Aug 30, 2008·Ecology·J Andrew Royle, Kevin V Young
May 20, 2009·Ecology·Beth GardnerMichael T Wegan
Jul 25, 2009·Statistics in Medicine·David LunnNicky Best
Jan 1, 1946·Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences·H JEFFREYS

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Citations

Mar 10, 2016·Biometrics·Daniel Manrique-Vallier
Jul 29, 2015·Ecological Applications : a Publication of the Ecological Society of America·Brian D Gerber, Robert R Parmenter
Feb 16, 2019·Ecology and Evolution·Gurutzeta Guillera-ArroitaJosé J Lahoz-Monfort
Nov 20, 2016·Ecology·Kristin M BromsRyan M Fitzpatrick

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