polyagamma 0.1.0rc1

Efficiently sample from the Polya-Gamma distribution using NumPy's Generator interface

polya-gamma

Efficiently sample from the Polya-Gamma distribution using NumPy's Generator interface.

Dependencies

• Numpy >= 1.17

Installation

$ pip install -U polyagamma

Example

Python

polyagamma can act as a drop-in replacement for numpy's Generator class.

import numpy as np

from polyagamma import default_rng, Generator

g = Generator(np.random.PCG64())  # or use default_rng()
print(g.polyagamma())

# Get a 5 by 10 array of PG(1, 2) variates.
print(g.polyagamma(z=2, size=(5, 10)))

# Pass sequences as input. Numpy's broadcasting semantics apply here.
h = [[1, 2, 3, 4, 5], [9, 8, 7, 6, 5]]
print(g.polyagamma(h, 1))

# Pass an output array
out = np.empty(5)
g.polyagamma(out=out)
print(out)

# one can choose a sampling method from {devroye, alternate, gamma}.
# If not given, the default behaviour is a hybrid sampler that picks
# the best method based on the parameter values
out = g.polyagamma(method="devroye")

# other numpy distributions are still accessible
print(g.standard_normal())
print(g.standard_gamma())

C

For an example of how to use polyagamma in a C program, see here.

TODO

• Add devroye and gamma convolution methods.
• Add the "alternate" sampling method.
• Add the hybrid sampler based on a combination of available methods.
• Add the "saddle point approximation" method.
• Add the hybrid sampler based on all four methods.
• Add array broadcasting support for paramater inputs.

References

• Luc Devroye. "On exact simulation algorithms for some distributions related to Jacobi theta functions." Statistics & Probability Letters, Volume 79, Issue 21, (2009): 2251-2259.
• Polson, Nicholas G., James G. Scott, and Jesse Windle. "Bayesian inference for logistic models using Pólya–Gamma latent variables." Journal of the American statistical Association 108.504 (2013): 1339-1349.
• J. Windle, N. G. Polson, and J. G. Scott. "Improved Polya-gamma sampling". Technical Report, University of Texas at Austin, 2013b.
• Windle, Jesse, Nicholas G. Polson, and James G. Scott. "Sampling Polya-Gamma random variates: alternate and approximate techniques." arXiv preprint arXiv:1405.0506 (2014)