**Sankhya:
The Indian Journal of Statistics**

2004, Volume 66, Pt. 3, 487--512

**Properties of Right Haar
Predictive Inference**

By

Morris L. Eaton and William D. Sudderth, University of Minnesota, USA

SUMMARY. Consider an invariant prediction problem where the group is transitive on the parameter space. The Haar predictive distribution (Haar inference) is obtained as the formal predictive distribution using the right Haar measure as a prior. This Haar inference is discussed in three different contexts: model matching, Fisherian pivoting, and de Finetti's coherence. It is shown that the Haar inference enjoys exact probability matching for highest probability density (HPD) regions. Fisherian pivotal distributions agree with Haar inference when pivoting is possible. Further any invariant inference that is essentially different from the Haar inference is incoherent.

*AMS (1991) subject classification}. ***62H05, 62H99, 62A05, 62A30**.

*Key words and phrases. *Coherence, Dutch book, Fisherian pivoting,
invariant predictive distributions, right Haar inference, strong inconsistency.