# Elicitation, measuring bias, checking for prior-data conflict and inference with a Dirichlet prior

## TL;DR

This paper develops methods for eliciting and assessing Dirichlet priors based on bounds, enabling bias measurement, prior-data conflict checking, and hypothesis evaluation in contingency table analysis.

## Contribution

It introduces a novel approach to prior elicitation using bounds on probabilities and integrates bias assessment and conflict checking into Bayesian inference.

## Key findings

- Effective prior elicitation based on bounds
- Methods to detect prior-data conflict
- Relative belief approach for hypothesis assessment

## Abstract

Methods are developed for eliciting a Dirichlet prior based upon bounds on the individual probabilities that hold with virtual certainty. This approach to selecting a prior is applied to a contingency table problem where it is demonstrated how to assess the bias in the prior as well as how to check for prior-data conflict. It is shown that the assessment of a hypothesis via relative belief can easily take into account what it means for the falsity of the hypothesis to correspond to a difference of practical importance and provide evidence in favor of a hypothesis.