Tools for non-Gaussian statistics
gaussfree is a library aiming at offering tools for
Statistical operations in situations where the Gaussian ditribution is not correct;
Estimation of distirbution parameters avoiding the normal approximation;
Bayesian inference; and
Additional helper and visualization functions.
While it is far from complete, or generic, in its current implementation, this is the ultimate goal of the project.
The API is explained in detail in the official documentation:
Features
For now, the features are rather dedicated to a specific project, but there are plans to extend and generalize them.
Feature 1: Estimation of the binomial parameter \(p\) (success probability), with arbitrary prior distribution.
Feature 2: Construction of unimodal Beta distributions with a specific mode and variance.
Installation
Simply download or clone the source, switch to your favourite environment, and run
pip install .
from the top level of the repository.
For the Sphinx autogenerated documentation, install via ``pip`` the following packages: ``sphinx_mdinclude``, ``sphinx-math-dollar`` and ``sphinx-rtd-theme``.
Examples
Construct a unimodal Beta distribution
from gaussfree.distributions.beta import get_unimodal_beta
my_prior = get_unimodal_beta(mode=0.75, variance=0.03, verbose=True)
Estimate the binomial \(p\)
from gaussfree.estimation.binomial import EstimateBinomialP
est = EstimateBinomialP(3, 2) # trials n=3, successes k=2
est.report() # print result and show posterior
# plot the 68% highest-posterior density interval
plt.errorbar(0.0, est.mode, yerr=[[est.err_lo], [est.err_hi]])
print(f"Posterior mean+/-std: {est.mean:.3f} +/- {est.std:.3f}")
with_prior = EstimateBinomialP(3, 2, prior_dist=my_prior)
License
This project is licensed under the MIT License. See the LICENSE file for details.
Acknowledgements
I would like to thank Grigoris Maravelias for suggesting publishing my contribution to his paper [https://ui.adsabs.harvard.edu/abs/2025arXiv250401232M/abstract], and his idea on being just the starting point for a more general package.