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Nested Sampling

Source code: https://github.com/js850/nested_sampling

Documentation: http://js850.github.io/nested_sampling

Flexible and efficient Python implementation of the nested sampling algorithm. This implementation is geared towards allowing statistical physicists to use this method for thermodynamic analysis but is also being used by astrophysicists.

This implementation uses the language of statistical mechanics (partition function, phase space, configurations, energy, density of states) rather than the language of Bayesian sampling (likelihood, prior, evidence). This is simply for convenience, the method is the same.

The package goes beyond the bare implementation of the method providing:

  • built-in parallelisation on single computing node (max total number of cpu threads on a single machine)
  • built-in Pyro4-based parallelisation by distributed computing, ideal to run calculations on a cluster or across a network
  • ability to save and restart from checkpoint binary files, ideal for very long calculations
  • scripts to compute heat capacities and perform error analysis
  • integration with the MCpele package to implement efficient Monte Carlo walkers.
nested_sampling.jpg

Figure 1: Snapshot of a Nested Sampling iteration on a multimodal surface. Each contour line corresponds to a past maximum energy (log-likelihood) constraint. The inner most contour line corresponds to the current constraint and the corresponding sample is removed (crossed in red) and replaced by walking a copy of a randomly selected replica (walk trajectory is the dashed line and the red point is the new configuration that satisfies the tighter constraint). The bottom panel shows the fraction of phase space corresponding to each sample and the iterative contractions (corresponding to the contours) are shown by the horizontal lines. Note that the nested sampling contraction of phase space is constant in the log of phase space volume. The full animation can be run from the example folder.

nested sampling has been authored by Stefano Martiniani Jacob D. Stevenson at the University of Cambridge. The project is publicly available under the GNU general public licence.

INSTALLATION

Required packages

for compilation:

  1. c/c++ compiler

python packages:

  1. numpy:
    We use numpy everywhere for doing numerical work.
  2. matplotlib:
    For making plots
  3. cython:
    For interfacing c/c++ to Python
  4. Pyro4: optional
    for distributed parallelisation

All the above packages can be installed via the python package manager pip (or easy_install), with the exception of pele. However, some of the packages (numpy, scipy) have additional dependencies and it can be more convenient to use the linux package manager (apt, yum, ...).

Installing prerequisites on Ubuntu

If you're running ubuntu, you can get all the prerequisites with the following commands:

$ sudo apt-get install python-numpy python-matplotlib python-pip cython
$ pip install --user pyro4

Compilation

Compilation is required for the heap capacity routines and possibly for Monte Carlo walkers if these make use of more efficient c++ routines This package uses the standard python setup utility (distutils). There are lots of options for how and where to install. For more information:

$ python setup.py --help
$ python setup.py --help-commands

Developers probably want to install "in-place", i.e. build the extension modules in their current directories:

$ python setup.py build_ext -i

Users can install pele in the standard python package location:

$ python setup.py build
$ python setup.py install [--user]

where --user installs it in $HOME/.local/

PYTHONPATH

If you do an in-place install, make sure to add the install directory to your PYTHONPATH environment variable. This is not necessary if you install to a standard location.

Running

You can find examples of how to run nested sampling in the examples folder. More information can be found in the documentation at

http://js850.github.io/nested_sampling

Tests

Nested sampling has a suite of unit tests. They can be run using the nose testing framework (which can be installed using pip). The tests are run from the top directory with this command:

nosetests nested_sampling

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python based implementation of the nested sampling algorithm

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