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Global-Local Mixtures

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.