Discordance between prior and data using conjugate priors

In Bayesian Inference the choice of prior is very important to
indicate our beliefs and knowledge. However, if these initial beliefs
are not well elicited, then the data may not conform to our
expectations. The degree of discordancy between the observed data and
the proper prior is of interest. Pettit and Young (1996) suggested a
Bayes Factor to find the degree of discordancy. I have extended their
work to further examples.

I try to find explanations for Bayes Factor behaviour. As an
alternative I have looked at a mixture prior consisting of the
elicited prior and another with the same mean but a larger variance.
The posterior weight on the more diffuse prior can be used as a
measure of the prior and data discordancy and also gives an automatic
robust prior. I discuss various examples and show this new measure is
well correlated with the Bayes factor approach.