Log-linear modelling plays an important role in many statistical
applications, particularly in the analysis of contingency table data.With the
advent of powerful new computational techniques such as reversible jump MCMC,
Bayesian analyses of these models, and in particular model selection and
averaging, have become feasible. Coupled with this is the desire to construct
and use suitably flexible prior structures which allow efficient computation
while facilitating prior elicitation. The latter is greatly improved in the
case where priors can be specified on interpretable parameters about which
relevant experts can express their beliefs.
¶ In this paper, we show how the specification of a general
multivariate normal prior on the log-linear parameters induces a multivariate
log- normal prior on the corresponding cell counts of a contingency table. We
derive the parameters of this distribution in an explicit practical form and
state the corresponding mean and covariances of the cell counts. We discuss the
importance of these results in terms of applying both uninformative and
informative priors to the model parameters and provide an illustration in the
context of the analysis of a 23 contingency table.