WITHDRAWN Eliciting some generalisations of Dirichlet distribution as priors for Multinomial models

Music City Center 

The Dirichlet distribution, central to probability theory and statistical modeling, is a cornerstone for multinomial sampling models. Its ability to simulate proportions across categories makes it indispensable in fields like biology and communication theory. However, as our understanding of complex systems advances, there is a need to extend and generalise models to better capture real-world intricacies. Hence, researchers have introduced some generalisations of the Standard Dirichlet such as the Dirichlet Type 3, Scaled Dirichlet, Shifted-scaled Dirichlet, Flexible Dirichlet and Extended Flexible Dirichlet distributions. These models provide greater flexibility in capturing dependencies and expert beliefs in elicitation contexts. While eliciting the standard Dirichlet distribution is well documented, methods for eliciting these more flexible models are relatively new. To support this, we have developed methods and a Shiny R application that enables experts to input and visualise their beliefs using these generalisations. This tool offers a practical approach to applying these advanced models, that supports the elicitation process and broadens their use in applied research.

Bayesian Statistics

Prior Elicitation

Expert Elicitation

Dirichlet Distribution

Shiny R 

IMS