A Pythonic implementation of the Nested Sampling integration algorithm for Bayesian model comparison and parameter estimation.

This package provides multiple implementations for constrained drawing functions, and a test suite to evaluate the correctness, accuracy and efficiency of various implementations.

The source code consists of three components:

1. A Modular framework for nested sampling algorithms (nested_sampling) and their development
2. Test framework to evaluate the performance and accuracy of algorithms (testsuite)
3. UltraNest - A fast C implementation of a mixed RadFriends/MCMC nested sampling algorithm

For drawing uniformly above the likelihood constraint, currently the following algorithms are implemented:

• naive rejection sampling
• MCMC with adaptive proposal
• RadFriends/SupFriends (see Buchner, 2014)
• SVM-based constrainer
• Galilean (in progress)
• Hamiltonian (in progress)

For testing the correctness and efficiency of algorithms, multiple algorithms can be run against a set of test problems.

Additionally to nested sampling implemented here, the following algorithms are evaluated in the benchmark:

• MultiNest (through PyMultiNest)
• Cuba-based algorithms (through PyCuba)
  • Suave
  • Divonne (through PyCuba)
  • Cuhre (through PyCuba)
  • Vegas (through PyCuba)

The evaluation of various algorithms can be found at https://johannesbuchner.github.io/UltraNest/testsuite/

UltraNest is a fast C implementation of a mixed RadFriends/MCMC nested sampling algorithm. It is documented at https://johannesbuchner.github.io/UltraNest/ultranest/ You are welcome to dive into the code (ultranest folder) and implement your preferred algorithm.

Have a look at the file nested_sampling/test/simplenested_test.py to build your own combination of nested sampling algorithm components.

You can run the entire test suite using the testsuite/testbase.py but to only run a part of it create skip_algorithms and skip_problems files and run testsuite/partialtestbase.py

The documentation is available at https://johannesbuchner.github.io/UltraNest/ The source code repository is available at https://github.com/JohannesBuchner/UltraNest/

The correct citation to use is Buchner (2014) published in Statistics and Computing (Journal article, Preprint PDF).

BibTeX:

@Article{Buchner2014stats,
  Title                    = {{A statistical test for Nested Sampling algorithms}},
  Author                   = {Buchner, Johannes},
  Year                     = {2014},
  Doi                      = {10.1007/s11222-014-9512-y},
  Eprint                   = {1407.5459},
  ISSN                     = {0960-3174},
  Language                 = {English},
  Month                    = jul,
  Pages                    = {1-10},

  Adsnote                  = {Provided by the SAO/NASA Astrophysics Data System},
  Adsurl                   = {http://adsabs.harvard.edu/abs/2014arXiv1407.5459B},
  Archiveprefix            = {arXiv},
  Journal                  = {Statistics and Computing},
  Keywords                 = {Nested sampling; MCMC; Bayesian inference; Evidence; Test; Marginal likelihood},
  Owner                    = {user},
  Primaryclass             = {stat.CO},
  Publisher                = {Springer US},
  Timestamp                = {2014.08.20}
}

This work is open source software licensed under GPLv3 Affero (see LICENSE file). If you are interested in a different license, please contact me.