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

Area of Science:

• Ecology
• Statistics
• Wildlife Biology

Background:

• Wildlife population size estimation often uses binomial counts.
• Bayesian analysis commonly employs a constant prior for population size (N) to remain uninformative.
• Data augmentation methods utilize super-populations and individual detection probabilities.

Purpose of the Study:

• To demonstrate paradoxical and unacceptable features of the constant prior for population size estimation.
• To introduce and advocate for the use of the scale prior as a superior alternative.
• To illustrate the implementation of the scale prior in OpenBUGS for data augmentation.

Main Methods:

• Analysis of Bayesian methods for population size estimation.
• Demonstration of the mathematical properties of constant priors.
• Application of the scale prior in statistical modeling and OpenBUGS software.
• Utilizing data augmentation with individual covariates.

Main Results:

• The constant prior exhibits paradoxical and unacceptable characteristics in population size estimation.
• The scale prior avoids the defects of the constant prior and shows good frequentist performance.
• The scale prior can be effectively approximated and implemented in OpenBUGS.

Conclusions:

• The constant prior is unsuitable for wildlife population size estimation.
• The scale prior is a robust and recommended alternative for Bayesian population modeling.
• The scale prior facilitates advanced analyses, including data augmentation with covariates.