PolyaGammaSamplers.jl

PolyaGammaSamplers.jl provides a method for sampling from the Polya-Gamma distribution ([1]), using the Distributions.jl interface. The Polya-Gamma distribution with parameters b > 0 and z ≥ 0 has Laplace transform

\[\begin{aligned} \mathcal{L}(t) = \cosh^b(z) \cosh^{-b}(\sqrt{2t + z^2}). \end{aligned}\]

This distribution is useful for learning Bayesian Logit, Negative Binomial and non-parametric models ([1, 2, 3]).

Currently, the only available sampler is the one proposed in [1] (hereafter, the PSW sampler).

References

1. https://doi.org/10.1080/01621459.2013.829001.
2. https://arxiv.org/pdf/1206.6456.
3. https://doi.org/10.1016/j.jspi.2020.05.009.
4. https://arxiv.org/abs/1405.0506.