This is my masters’ thesis at the University of Cambridge.
The corresponding article is given in \LaTeX form.
This repository contains the general framework for using Stochastic superpositional mixture repartitioning, as a technique to improve robustness and performance of nested sampling.
It was designed for PolyChord, and the currently present framework directly depends on it, however it can be adapted to work with any nested sampling library.
This contains some benchmark results in PGF format, and can be viewed if you compile the article using \LaTeX.
All of the figures were produced using the provided programs. For
each illustration the .py file with the corresponding name
produces it. Keep in mind that the benchmark takes over a day to
complete.
Illustrations without dependencies are in the same folder, while
ones that refer to polychord, are in the framework folder.
All dependencies besides PolyChord are pip installable.
Simply put, to do Bayesian inference you should have a prior, and a
likelihood. To provide your own, subclass Model from
polychord_model.
You will need to provide a quantile function, which maps from the unit hyper-cube onto the (which they are related to, but are not themselves). The LogLikelihood also needs to be specified, and it follows the conventions of PolyChord.
Models of this kind can be model.nested_sample‘d, where you can specify
the settings for PolyChord.
Examples of use are provided in .framework/benchmarks.py.
In short, Bayesian inference using a uniform (and otherwise) prior
can be sped up, while Bayesian inference using a Gaussian Prior made
more robust by a technique called Posterior Repartitioning (details
in project-report.org). There was, as of this writing, only one
such documented method.
The included paper discusses the general requirements one needs to satisfy in order to have successfully come up with a repartitioning scheme. Also, included, is a scheme I have devised: stochastic superpositional mixture repartitioning. What this allows you to do, is to combine different schemes together. It’s intelligent enough to make use of the representative priors in the mixture and ignore the unrepresentative ones.
It’s abstract, in that it does not set restrictions beyond the ones you already needed to satisfy to use your prior.
According to my benchmarks, it’s remarkably performant. It is also more stable to perturbations than Power Posterior Repartitioning, (the documented method, also implemented here).
The cobaya submodule contains the modified version of Cobaya, that makes use of Posterior repartitioning. It was tested on the CSD3 cluster, so beware of attempting this at home.
Will Handley et al. : Polychord, Anesthetic, project supervisor. Anthony Lewis, Cobaya