Sampling Polya-Gamma random variates: alternate and approximate techniques

Efficiently sampling from the P'olya-Gamma distribution, $PG(b,z)$, is an essential element of P'olya-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.