  Global-local mixtures are derived from the Cauchy-Schlomilch and Liouville
integral transformation identities. We characterize well-known normal-scale
mixture distributions including the Laplace or lasso, logit and quantile as
well as new global-local mixtures. We also apply our methodology to
convolutions that commonly arise in Bayesian inference. Finally, we conclude
with a conjecture concerning bridge and uniform correlation mixtures.
