pybalonor

This Python package helps to perform a Bayesian analysis of log-normally distributed data (PYthon package for Bayesian Analysis of the LOg-NORmal distribution). Performing a Bayesian analysis of log-normally distributed data requires care in the prior choice to yield posterior predictive distributions with finite moments (e.g. Fabrizi & Trivisano, 2012).

This package uses a simple uniform prior for the log-location and log-variance parameter. The problem of normalizing the posterior of the mean is solved by imposing a finite upper bound on the log-variance parameter.

Preface

If you are looking for an analysis of the log-normal distribution, you might likely want to check out the R package BayesLN by Gardini, Fabrizi, and Trivisano. Their conjugate prior is more sophisticated than the flat prior of pybalonor, and, from limited analysis, seems to lead to tighter posterior bounds.

If instead you are looking for an analysis based on a flat prior, looking for a Python solution, or working with a large data set, go ahead!

Installation and Requirements

The following software is required to install pybalonor:

• A modern C++ compiler
• Boost Math (v1.80.0 or later recommended for numerical stability)
• The Meson build system
• Cython
• NumPy
• Mebuex

The Python package can be built from the repository's root directory using the setuptools build system. For instance, you may call the following command from the repository's root directory:

pip install --user .

Usage

Currently, pybalonor provides one class, CyLogNormalPosterior:

class CyLogNormalPosterior:
    def __init__(self, X, l0_min, l0_max, l1_min, l1_max):
        pass

    def log_posterior(self, l0, l1):
        pass

    def log_posterior_predictive(self, x):
        pass

    def posterior_predictive(self, x):
        pass

    def posterior_predictive_cdf(self, x):
        pass

    def log_mean_posterior(self, mu):
        pass

The parameters are as follows:

Parameter	Type	Purpose
X	dbuf1	The data set.
x	dbuf1	Where to evaluate the posterior predictive (same dimension as X).
mu	dbuf1	Log-Normal distribution mean (evaluated as density over the posterior)
l0	dbuf1	Log-location parameter $l_0$ at which to evaluate the posterior.
l1	dbuf1	Log-variance parameter $l_1$ (like l0)
l0_min	float	Minimum of log-location parameter for prior.
l0_max	float	Maximum of log-location parameter.
l1_min	float	Minimum of log-variance parameter for prior.
l1_max	float	Maximum of log-variance parameter.

Note: dbuf1 refers to a C-contiguous buffer of doubles (e.g. a one-dimensional NumPy array).

For more information, visit the pybalonor documentation.

Citation

If you use pybalonor for scientific work, you may cite the specific version on Zenodo:

Ziebarth, Malte Jörn. (2023). pybalonor: A package for the Bayesian analysis of the log-normal distribution in Python. (1.0.0). Zenodo. https://doi.org/10.5281/zenodo.7896869

License

This software is licensed under the European Public License (EUPL) version 1.2 or later (EUPL-1.2). See the LICENSE file in this directory.

Changelog

The format is based on Keep a Changelog, and this project adheres to Semantic Versioning.

[1.0.0] - 2023-05-04

Added

• Initial release.