Eliciting univariate priors for binomial sampling models: beyond the beta distribution

Bayesian analysis provides a robust way to incorporate prior knowledge into statistical models, but eliciting diverse subjective priors for parameters in the unit interval [0, 1] remains lacking. These priors are vital for modelling probabilities, proportions, and success rates in many real-world applications. Beta distribution, although popular for its simplicity and conjugacy to the binomial models, may not always capture the true prior beliefs in certain real-world applications. This paper explores eliciting some alternative informative priors for binomial sampling models, beyond the conventional usage of the Beta distribution. We have developed an interactive Shiny R application to support the elicitation process of 14 different prior distributions. This tool helps users to visualise, compare priors and see their characteristics and perform a full prior-to-posterior Bayesian analysis for binomial models. In three important examples, we demonstrate elicitation processes for estimating the presence of a plant species, Fritillaria meleagris , in a meadow ecosystem; the probability of Drosophila melanogaster egg hatching under mutation and of passive transfer success in neonatal foals.