Python toolkit for Nested Sampling.

# Gleipnir

Gleipnir is a python toolkit that provides an easy to use interface for Bayesian parameter inference and model selection using Nested Sampling. It has a built-in implementation of the Nested Sampling algorithm but also provides a common interface to the Nested Sampling implementations MultiNest, PolyChord, dyPolyChord, DNest4, and Nestle. Although Gleipnir provides a general framework for running Nested Sampling simulations, it was created with biological models in mind. It therefore supplies additional tools for working with biological models in the PySB format (see the PySB Utilities section). Likewise, Gleipnir's API was designed to be familiar to users of PyDREAM and SimplePSO, which are primarily used for biological model calibration.

### What is Nested Sampling?

Nested Sampling is a numerical integration scheme for estimating the marginal likelihood, or in Nested Sampling parlance, the 'evidence' of high-dimensional models. As a side-effect of the evidence calculation, estimates of the posterior probability distributions of model parameters can also be generated.

In particular, Nested Sampling was designed to handle evaluate the evidence of high-dimensional models where the likelihood is exponentially localized in the prior probability mass. In the Nested Sampling approach, the evidence is first converted from a (possibly) multi-dimensional integral into a one-dimensional integral taken over a mapping of the likelihood function to elements of the unit prior probability mass (X). In principle, this is achieved by using a top-down approach in which sample points are drawn according to the prior distribution, and the unit prior probability is subdivided into equal fractional elements from X = 1 down to X = 0 and mapped to the likelihood function, L(X), via a likelihood sorting routine.

The Nested Sampling method was originally developed by John Skilling; see the following references:

1. Skilling, John. "Nested sampling." AIP Conference Proceedings. Vol. 735. No. 1. AIP, 2004.
2. Skilling, John. "Nested sampling for general Bayesian computation." Bayesian analysis 1.4 (2006): 833-859.
3. Skilling, John. "Nested sampling’s convergence." AIP Conference Proceedings. Vol. 1193. No. 1. AIP, 2009.

# Install

! Warning
Gleipnir is still under heavy development and may rapidly change.

Gleipnir installs as the gleipnir package. It is compatible with Python 3.6.

#### conda install

Although not absolutely required, we recommend using the Anaconda Python distribution and the conda package manager.

gleipnir can be installed from the terminal using conda:

conda intall -c blakeaw gleipnir


Note that gleipnir has the following core dependencies which will also be installed:

Alternatively, for convenience, a gleipnir environment can be downloaded/created that has gleipnir, its core dependencies, as well as several optional/recommended packages; the optional/recommended packages include pysb, hypbuilder, matplotlib, seaborn, and jupyter. From the terminal:

conda env create blakeaw/gleipnir


and then activate it with:

conda activate gleipnir


Additionally, there is another gleipnir environment for linux-64 that can be downloaded/created that has gleipnir, its core dependencies, as well as most of the recommended additional software packages; note that the versions of packages are pinned to exact version numbers in this environment file. From the terminal:

conda env create blakeaw/gleipnir-all-linux64


and then activate it with:

conda activate gleipnir


#### pip install

You can install the gleipnir package using pip sourced from the GitHub repo:

pip install -e git+https://github.com/LoLab-VU/Gleipnir@v0.18.0#egg=gleipnir


However, this will not automatically install the core dependencies. You will have to do that separately:

pip install numpy scipy pandas


The following software is not required for the basic operation of Gleipnir, but provides extra capabilities and features when installed.

#### PySB

PySB is needed to run PySB models and it is needed if you want to use the gleipnir.pysb_utilities module:

conda install -c alubbock pysb


#### HypBuilder

If you want use the HypSelector class from gleipnir.pysb_utilities then you need to have HypBuilder:

conda install -c blakeaw hypbuilder


#### Jupyter

If you want to run the Jupyter IPython notebooks that come with Gleipnir then you need to install Jupyter:

conda install jupyter


#### Plotting packages:

We recommend installing Matplotlib and seaborn to generate plots. Note that some of the Gleipnir examples will use these packages if they are installed to generate sample plots. Matplotlib is also needed for one of the Jupyter notebooks.

conda install matplotlib seaborn


#### MultiNest

If you want to run Nested Sampling simulations using Gleipnir's MultiNest interface class object, MultiNestNestedSampling (from the gleipnir.multinest module), then you will need to install PyMultiNest and MultiNest. Build and install instructions for getting PyMultiNest and MultiNest from source can be found at: http://johannesbuchner.github.io/PyMultiNest/install.html

PyMultiNest is available on PyPI:

pip install pymultinest


Note that in addition to MultiNest, pymultinest requires numpy, scipy, and matplotlib to run. It also optionally requires mpi4py to run MultiNest with MPI parallelization.

You can get a linux-64 conda build of MultiNest from the blakeaw conda channel:

conda install -c blakeaw multinest


Note that this conda build of MultiNest requires packages from the anaconda and conda-forge channels, so you'll need to add them to the channel list in your conda config (.condarc) file. You can also install a build of mpi4py that is compatible with this build of multinest from the blakeaw conda channel:

conda install -c blakeaw mpi4py


Additionally, a separate set of third party instructions for building and installing on Mac OS can be found at: http://astrobetter.com/wiki/MultiNest+Installation+Notes

Also, this PyMultiNest GitHub issue may be helpful if you run into library path problems on Mac OS: https://github.com/JohannesBuchner/PyMultiNest/issues/89

#### PolyChord

If you want run Nested Sampling simulations using PolyChord via the PolyChordNestedSampling class from the gleipnir.polychord, then you will need to install pypolychord (for PolyChordLite version >= 1.16). Build and install instructions are in the README at: https://github.com/PolyChord/PolyChordLite

However, as per PolyChordLite GitHub Issue 11 there is a version of pypolychord on PyPI which should work for linux-64:

pip install pypolychord


But note that the current version of pypolychord on PyPI (as of 07-01-2019) is not the most recent version, and some of the extra functionality provided by Gleipnir will not work with it.

Special Notes for builds from source on linux-64:

• Installs into your .local/lib python site-packages.
• Requires gfortran (f77 compiler) and lipopenmpi-dev (development libraries for MPI) to build the code.

#### dyPolyChord

If you want to run Nested Sampling simulations using dyPolyChord using Gleipnir's interface object, dyPolyChordNestedSampling (from the gleipnir.dypolychord module), then you will need to install dyPolyChord (available on PyPI):

pip install dyPolyChord


Note that dyPolyChord requires PolyChord to run, so its use via Gleipnir requires the pypolychord package; see the the previous section. Also note that in addition to PolyChord, dyPolyChord requires numpy, scipy, and nestcheck to run. It also optionally requires mpi4py to run with MPI parallelization. For additional information check out the dyPolyChord documentation.

#### DNest4

If you want run Nested Sampling simulations using DNest4 via the DNest4NestedSampling class from the gleipnir.dnest4 module, then you will need to get DNest4 and its Python bindings. Instructions for building and installing from source can be found in the README at: https://github.com/eggplantbren/DNest4

Additionally, a linux-64 conda build of dnest4 can be installed from the blakeaw conda channel:

conda install -c blakeaw dnest4


Special Notes for building and installing from source:

• Requires a c++ compiler with c++11 standard libraries.
• Requires Cython and numba for python bindings to compile and install

#### Nestle

If you want to run Nested Sampling simulations using Nestle via Gleipnir's interface object, NestleNestedSampling (from the gleipnir.nestle module), then you will need to install Nestle (available on PyPI):

pip install nestle


Note that Nestle requires numpy to run (also required for gleipnir), and it also optionally requires scipy.

For additional information check out the Nestle documentation.

# Documentation and Usage

Checkout the Jupyter Notebooks (more in the pipeline):

Also checkout the examples to see example scripts that show how to setup Nested Sampling runs using Gleipnir.

# Contact

To report problems or bugs please open a GitHub Issue. Additionally, any comments, suggestions, or feature requests for Gleipnir can also be submitted as a GitHub Issue.

# PySB Utilities

## nestedsample_it

nestedsample_it is a utility that helps generate a Nested Sampling run script or NestedSampling objects for a PySB model.

### Commmand line use

nestedsample_it can be used as a command line utility to generate a template Nested Sampling run script for a PySB model. nestedsample_it reads the model file, imports and pulls out all the kinetic parameters, and then writes out a run_NS script for that model. nestedsample_it currently writes out a run script for classic Nested Sampling via Gleipnir, so you'll need to modify it to use one of the other Nested Samplers (MultiNest, PolyChord, or DNest4). And you will need to edit the run script to load any data and modify the loglikelihood function, but nestedsample_it should give you a good starting point.

Run nestedsample_it from the command line with following format:

python -m glepnir.pysb_utilities.nestedsample_it model.py output_path


where output_path is the directory/folder location where you want the generated script to be saved.

The command line version of nestedsample_it also has support for a limited set of #NESTEDSAMPLE_IT directives which can be added to model files. The current directives are:

• #NESTEDSAMPLE_IT prior [param_name, param_index] [norm, uniform]
• Specify the type of prior to assign to a parameter. The parameter can either be specified by its name or its index (in model.parameters). The priors that can be assigned are either norm or uniform; note that uniform is the default for all parameters.
• #NESTEDSAMPLE_IT no-sample [param_name, param_index]
• Specify a fixed parameter (i.e., not to included in sampling). The parameter can either be specified by its name or its index (in model.parameters).

### Progammatic use via the NestedSampleIt class

The nestedsample_it utility can be used progammatically via the NestedSampleIt class. It's importable from the pysb_utilities module:

from gleipnir.pysb_utilities import NestedSampleIt


The NestedSampleIt class can build an instance of a NestedSampling object.
Here's a faux minimal example:

from my_pysb_model import model as my_model
from gleipnir.pysb_utilities import NestedSampleIt
import numpy as np

timespan = np.linspace(0., 10., 10)
observable_data = dict()
time_idxs = list(range(len(timespan)))
observable_data['my_observable'] = (data, data_sd, time_idxs)
# Initialize the NestedSampleIt instance with the model details.
sample_it = NestedSampleIt(my_model, observable_data, timespan)
# Now build the NestedSampling object. -- All inputs are
# optional keyword arguments.
nested_sampler = sample_it(ns_version='gleipnir-classic',
ns_population_size=100,
ns_kwargs=dict(),
log_likelihood_type='logpdf')
# Then you can run the nested sampler.
log_evidence, log_evidence_error = nested_sampler.run()


NestedSampleIt constructs the NestedSampling object to sample all of a model's kinetic rate parameters. It assumes that the priors are uniform with size 4 orders of magnitude and centered on the values defined in the model.

In addition, NestedSampleIt crrently has three pre-defined loglikelihood functions with different estimators. They can be specified with the keyword parameter log_likelihood_type:

# Now build the NestedSampling object.
nested_sampler = sample_it(log_likelihood_type='logpdf')


The options are

• 'logpdf'=>Compute the loglikelihood using the normal distribution estimator
• 'mse'=>Compute the loglikelihood using the negative mean squared error estimator
• 'sse'=>Compute the loglikelihood using the negative sum of squared errors estimator. The default is 'logpdf'. Each of these functions computes the loglikelihood estimate using the timecourse output of a model simulation for each observable defined in the observable_data dictionary. If you want to use a different or more complicated likelihood function with NestedSampleIt then you'll need to subclass it and override one of the existing loglikelihood functions.

#### NestIt

The nestedsample_it module has a built-in helper class, NestIt, which can be used in conjunction of with NestedSampleIt class. NestIt can be used at the level of PySB model definition to log which parameters to include in a Nested Sampling run. It can be imported from the pysb_utilities module:

from gleipnir.pysb_utilities import NestIt


It is passed at instantiation to the NestedSampleIt class, which uses it to build the sampled parameters list and parameter mask for the likelihood function. See the following example files:

Note that if you flag a parameter for sampling without setting a prior, NestIt will by default assign the parameter a uniform prior centered on the parameter's value with a width of 4 orders of magnitude.

#### Builder class from pysb.builder

The Builder class from pysb.builder can also be used in conjunction with the NestedSampleIt class. The Builder class itself is a wrapper class that can be used to construct a PySB model and set parameter priors, logging them for sampling. Although this feature was originally intended for use with the BayesSB package, the NestedSampleIt class supports it as a logger for sampled parameters. The instance of the Builder is passed at instantiation to the NestedSampleIt class, which uses it to build the sampled parameters list and parameter mask for the likelihood function. See the following example files:

Note that you have to explicitly set a prior for each parameter that you want to sample when you add it your model with the builder.parameter function. If no prior is given the parameter won't be included as a sampled parameter in the Nested Sampling run.

## HypSelector

HypSelector is a tool for hypothesis selection using HypBuilder and Nested Sampling-based model selection. Models embodying different hypotheses (e.g., optional reactions) can be defined using the HypBuilder csv syntax. HypSelector then allows users to easily compare all the hypothetical model variants generated by HypBuilder by performing Nested Sampling to compute their evidences and thereby do model selection; HypSelector also provides functionality to estimate Bayes factors from the evidence estimates, as well as estimators for the Akaike, Bayesian, and Deviance information criteria computed from the Nested Sampling outputs. See the grouped reactions example or the HypSelector Example Jupyter Notebook to see example usage of HypSelector.

## ModelSelector

Similar to HypSelector, ModelSelector is a tool for PySB model selection using Nested Sampling-based model selection. ModelSelector allows users to easily compare model variants written in PySB and see which one may best explain a dataset by performing Nested Sampling to compute their evidences and thereby do model selection; ModelSelector also provides functionality to estimate Bayes factors from the evidence estimates, as well as estimators for the Akaike, Bayesian, and Deviance information criteria computed from the Nested Sampling outputs. See the ModelSelector Example Jupyter Notebook to see example usage of ModelSelector.

# Citing

If you use the Gleipnir software in your research, please cite it. You can export the Gleipnir citation in your preferred format from its Zenodo DOI entry.

Also, please cite the following references as appropriate for software used with/via Gleipnir:

#### Packages from the SciPy ecosystem

These include NumPy, SciPy, Pandas, and Matplotlib for which references can be obtained from: https://www.scipy.org/citing.html

#### PySB

1. Lopez, C. F., Muhlich, J. L., Bachman, J. A. & Sorger, P. K. Programming biological models in Python using PySB. Mol Syst Biol 9, (2013). doi:10.1038/msb.2013.1

#### MultiNest

1. Feroz, Farhan, and M. P. Hobson. "Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses." Monthly Notices of the Royal Astronomical Society 384.2 (2008): 449-463.
2. Feroz, F., M. P. Hobson, and M. Bridges. "MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics." Monthly Notices of the Royal Astronomical Society 398.4 (2009): 1601-1614.
3. Feroz, F., et al. "Importance nested sampling and the MultiNest algorithm." arXiv preprint arXiv:1306.2144 (2013).

#### PyMultiNest:

1. Buchner, J., et al. "X-ray spectral modelling of the AGN obscuring region in the CDFS: Bayesian model selection and catalogue." Astronomy & Astrophysics 564 (2014): A125.

#### PolyChord

1. Handley, W. J., M. P. Hobson, and A. N. Lasenby. "PolyChord: nested sampling for cosmology." Monthly Notices of the Royal Astronomical Society: Letters 450.1 (2015): L61-L65.
2. Handley, W. J., M. P. Hobson, and A. N. Lasenby. "POLYCHORD: next-generation nested sampling." Monthly Notices of the Royal Astronomical Society 453.4 (2015): 4384-4398.

#### DNest4

1. Brewer, B. J., Pártay, L. B., & Csányi, G. (2011). Diffusive nested sampling. Statistics and Computing, 21(4), 649-656
2. Brewer, B., & Foreman-Mackey, D. (2018). DNest4: Diffusive Nested Sampling in C++ and Python. Journal of Statistical Software, 86(7), 1 - 33. doi:10.18637/jss.v086.i07

#### Nestle

Cite the GitHub repo: https://github.com/kbarbary/nestle

#### seaborn

Reference can be exported from the seaborn Zeondo DOI entry

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