  The use of the conditional autoregressive framework proposed by Besag, York,
and Molli\'e (1991; BYM) is ubiquitous in Bayesian disease mapping and spatial
epidemiology. While it is understood that Bayesian inference is based on a
combination of the information contained in the data and the information
contributed by the model, quantifying the contribution of the model relative to
the information in the data is often non-trivial. Here, we provide a measure of
the contribution of the BYM framework by first considering the simple
Poisson-gamma setting in which quantifying the prior's contribution is quite
clear. We then propose a relationship between gamma and lognormal priors that
we then extend to cover the framework proposed by BYM. Following a brief
simulation study in which we illustrate the accuracy of our lognormal
approximation of the gamma prior, we analyze a dataset comprised of
county-level heart disease-related death data across the United States. In
addition to demonstrating the potential for the BYM framework to correspond to
a highly informative prior specification, we also illustrate the sensitivity of
death rate estimates to changes in the informativeness of the BYM framework.
