Sampling Polya-Gamma random variates: alternate and approximate techniques

Efficiently sampling from the Pólya-Gamma distribution, ${PG}(b,z)$, is an essential element of Pólya-Gamma data augmentation. Polson et. al (2013) show how to efficiently sample from the ${PG}(1,z)$ distribution. We build two new samplers that offer improved performance when sampling from the ${PG}(b,z)$ distribution and $b$ is not unity.

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