can be interpreted as the posterior probability that the $j$[th]{} GEV parameter varies spatially, which can be used to approximate the Bayes factor comparing these models. In the separate mixture prior fit, the posterior probability that the GEV parameters vary spatially was at least 0.99 for all three parameters.

We also aim to quantify changes in extreme quantiles. The $q$[th]{} quantile at location ${\mathbf{s}}$ is $\mu({\mathbf{s}}) + \sigma({\mathbf{s}}) [1-\log
(1/q)^{-\xi({\mathbf{s}})} ]/\xi({\mathbf{s}})$, which is also called the $1/(1-q)$ year return level. Figure \[fquanthist\] plots the posterior of various pointwise quantile levels. The large location and scale parameters lead to large medians in the southeast, while the 0.95 quantile is the largest in Florida due to the large shape parameter.

![Posterior mean and standard deviation of the 0.10, 0.50, and 0.95 quantiles for the historical simulation. All units are mm/h.[]{data-label="fquanthist"}](591f07.eps)

The difference between the historical and future scenarios is summarized in Figures \[fgevchange\] and \[fquantchange\]. The estimated GEV location and log scale parameters are larger for the future scenario for the majority of the spatial domain. The increase is the largest in Alabama, Georgia, and New England. The shape parameter also shows an increase in Alabama, but statistically significant decrease in Florida. 