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<p>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,&#xa0;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, <i>Fritillaria meleagris</i>, in a meadow ecosystem; the probability of <i>Drosophila melanogaster</i> egg hatching under mutation and of passive transfer success in neonatal foals.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月20日

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  • Nayana Unnipillai,
  • Fadlalla G. Elfadaly

摘要

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.