polyagamma 1.0.0b1

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.

As expected, the saddle method improves as h tends to infinity.

Features

• polyagamma is written in C and optimized for performance.
• It is flexible and allows the user to sample using one of 4 available methods.
• Input parameters can be scalars, arrays or both; allowing for easy generation of multi-dimensional samples without specifying the size.
• Random number generation is thread safe.
• The functional API resembles that of common numpy/scipy functions, therefore making it easy to plugin to existing libraries.

Dependencies

• Numpy >= 1.17

Installation

$ pip install -U polyagamma

Example

Python

import numpy as np
from polyagamma import polyagamma

o = polyagamma()

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

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

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

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

# We can also use an existing instance of `numpy.random.Generator` as a parameter.
# This is useful to reproduce samples generated via a given seed.
rng = np.random.default_rng(12345)
o = polyagamma(random_state=rng)

C

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

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)