margarine 0.1.0

Introduction

margarine:

Marginal Bayesian Statistics

Authors:

Harry T.J. Bevins

Version:

0.1.0

Homepage:

https://github.com/htjb/margarine

Documentation:

https://margarine.readthedocs.io/

Installation

The software should be installed via the git repository using the following commands in the terminal

git clone https://github.com/htjb/margarine.git # or the equivalent using ssh keys
cd margarine
python setup.py install --user

A pip install is coming soon.

Details/Examples

margarine is designed to make the calculation of marginal bayesian statistics feasible given a set of samples from an MCMC or nested sampling run.

An example of how to use the code can be found on the github in the jupyter notebook notebook/Tutorial.ipynb, alternatively in the compiled documentation or at here.

Health Warning

The code is still in development.

Currently the code assumes, when calculating marginal statistics, that the priors are uniformly distributed. If the priors are more complex then one of two approaches can currently be taken in order to use margarine to calculate the KL divergence and Bayesian Dimensionality:

a. Before training a density estimator on the samples you can transform them into the uniform parameter space. This could be as simple as inputting the logarithm of a log-uniformly distributed parameter or may require more complex transformations. Since the KL divergence and dimensionality are invariant under these types of transformations the subsequent values calculated with margarine will be equivalent to the values in the original parameter space.

b. In some instances there may not be an obvious transformation from the non-uniform parameter space defined by a complex prior to the uniform parameter space. In these cases a more manual approach can be taken to calculate the marginal statistics. In order to calculate the marginal statistics we need to be able to assess the log probability of both the prior and the posterior and when the prior is complex then we can use margarine to train a density estimator on both it and the posterior. This gives us access to the log pdfs and an example of this is shown below

from margarine.kde import KDE
from margarine.processing import _forward_transform

# theta is the posterior samples loaded in previously with weights=weights
# prior is the prior samples with weights=prior_weights

posterior_kde = KDE(theta, weights)
posterior_kde.generate_kde()
posterior_kde_samples = posterior_kde.sample(5000)

prior_kde = KDE(prior, prior_weights)
prior_kde.generate_kde()
prior_kde_samples = prior_kde.sample(5000)

posterior_logprob = posterior_kde.kde.logpdf(
        _forward_transform(
            posterior_kde_samples,
            posterior_kde.theta_min, posterior_kde.theta_max).T)

prior_logprob = prior_kde.kde.logpdf(
        _forward_transform(
            prior_kde_samples,
            prior_kde.theta_min, prior_kde.theta_max).T)

# prior_logprob and posterior_logprob may need masking where non finite.

logL = weights*posterior_logprob - prior_weights*prior_logprob
import tensorflow as tf
KL = tf.reduce_mean(logL)
dimensionality = 2*(tf.reduce_mean(logL**2) - tf.reduce_mean(logL)**2)

Documentation

The documentation is available at: https://margarine.readthedocs.io/

To compile it locally you can run

cd docs
sphinx-build source html-build

after cloning the repo and installing the relevant packages.

Licence and Citation

The software is available on the MIT licence.

If you use the code for academic purposes we request that you cite the paper currently in preparation as Bevins et al. in prep..

Requirements

The code requires the following packages to run:

• numpy

• tensorflow

• scipy

To compile the documentation locally you will need:

• sphinx

• numpydoc

To run the test suit you will need:

• pytest

Contributing

Contributions and suggestions for areas of development are welcome and can be made by opening a issue to report a bug or propose a new feature for discussion.