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Efficiently sampling from the P\'olya-Gamma distribution, ${PG}(b,z)$, is an essential element of P\'olya-Gamma data augmentation.
Saddlepoint approximations in statistics
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First passage times and sojourn density for Brownian motion in space and the exact Hausdorff measure of the sample path
Z. Ciesielski and S. J. Taylor · 1962
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Asymptotic Analysis
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Elements of Complex Variables
L. L. Pennisi · 1976
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Information and Exponential Families
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Edgeworth and saddle-point approximations with statistical applications
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Eigenvalue expansions for diffusion hitting times
J. T. Kent · 1980
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Saddle point approximations for the distribution of the sum of independent random variables
R. Lugannani and S. Rice · 1980
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Complex Variables and Applications
R. V. Churchill and J. W. Brown · 1984
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Non-uniform random variate generation
L. Devroye · 1986
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Saddlepoint Approximations
J. L. Jensen · 1995
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Lévy Processes and Infinitely Divisible Distributions
K.-I. Sato · 1999
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Probability laws related to the Jacobi theta and Riemann zeta functions, and brownian excursions
P. Biane, J. Pitman, and M. Yor · 2001
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Saddlepoint Approximations with Applications
R. W. Butler · 2007
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On exact simulation algorithms for some distributions related to Jacobi theta functions
L. Devroye · 2009
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Simulating random variables using moment generating functions and saddlepoint approximations
D. McLeish · 2010
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Random variate generation for the generalized inverse gaussian distribution
L. Devroye · 2012
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Bayesian inference for logistic models using Pólya-gamma latent variables
N. G. Polson, J. G. Scott, and J. Windle · 2013
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C. P. Robert and G. Casella · 2005
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J. Windle · 2013
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