An introduction to the imprecise Dirichlet model for multinomial data

The imprecise Dirichlet model (IDM) was recently proposed by Walley as a model for objective statistical inference from multinomial data with chances θ. In the IDM, prior or posterior uncertainty about θ is described by a set of Dirichlet distributions, and inferences about events are summarized by lower and upper probabilities. The IDM avoids shortcomings of alternative objective models, either frequentist or Bayesian. We review the properties of the model, for both parametric and predictive inferences, and some of its recent applications to various statistical problems.