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June 2015

The Ensemble Julia Package

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The Ensemble package implements in Julia various stochastic samplers based on the "stretch move" for ensembles of walkers described by Goodman & Weare (2010), and popularised in the emcee package from Foreman-Mackey, et al (2013).

In addition to a basic implementation of the Goodman & Weare MCMC algorithm in the EnsembleSampler module, this algorithm forms the basis of a number of other stochastic sampling algorithms:

  • A nested sampling algorithm based around the stretch move from Goodman & Weare in EnsembleNest.

  • A combination MCMC/Gibbs sampling method in EnsembleGibbs.

  • A parallel-tempered MCMC (PTMCMC) in EnsemblePTSampler that automatically tunes the chain temperature following an algorithm similar to Vousden, Farr, & Mandel (2016).

  • A bare-bones implementation of the kombine sampler described in Farr & Farr (in prep) in EnesmbleKombine. This module is missing the automatic burnin determination and the bells-and-whistles from the Python package described in that paper, but is a fully-functional multi-modal KDE sampler.

  • Various support libraries for stochastic sampling with these packages:

    • Computation of autocorrelation lengths following the spirit, if not the algorithm, of Goodman's implementation of Sokal's definition of the autocorrelation length in the module Acor.

    • Various useful re-parameterisations of constrained parameters to remove the constraints in the Parameterizations module. Most of these are taken from the Stan Users Manual.

    • A basic Powell's method optimiser in the Optimize module.

    • A stable implementation of the logsumexp function in the Stats module.

The Ensemble module exports these various sub-modules as top-level identifiers.