A cautionary note on using the scale prior for the parameter N of a binomial distribution

Statistical analysis of ecological data may require the estimation of the size of a population, or of the number of species with a certain population. This task frequently reduces to estimating the discrete parameter N representing the number of trials in a binomial distribution. In Bayesian methods, there has been a substantial amount of discussion on how to select the prior for N. We propose a prior for N based on an objective measure of the worth that each value of N has in being included in the model space. This prior is compared (through the analysis of the popular snowshoe hare dataset) with the scale prior which, in our opinion, cannot be understood from solid objective considerations.