Galilean Monte Carlo Nested Sampling

Implements Galilean Monte Carlo Nested Sampling in pure Julia, intended for arbitrary models with ordinary continuous parameter spaces.

Skilling, John. “Galilean and Hamiltonian Monte Carlo.” In Proceedings, 33:8. Garching, Germany: MDPI, 2019.

Installation

To install, add the github address in the Julia package manager (shortcut "]").

julia> ]add https://github.com/mmattocks

Example: Solving the Eggbox Problem

The eggbox problem uses the likelihood function log_lh=(2 + cos(5π * x1) * cos(5π * x2))^5, where x1 and x2 are the two parameters of the model, in the range 0:1. This gives a surface with 18 evenly spaced minima, the "eggbox". To solve it with GMC_NS.jl:

using GMC_NS, Distributions

#define the priors
prior=Uniform(0,1)
priors=[prior,prior]

#define the sampling box
box=[0. 1.
     0. 1.]

#use the package's default settings
gmc=GMC_DEFAULTS
gmc[1]=180 #change the minimum number of live particles to 160
gmc[2]=eps() #change the timestep at which particles are killed to be very small

#instantiate an ensemble with 1000 model-particles, given the priors, box, and GMC settings
e=Eggbox_Ensemble("Eggbox_test", 1000, priors, box, gmc...)

#define some displays to monitor the algorithm on-line
uds=Vector{Vector{Function}}([[evidence_display],[liwi_display],[convergence_display]])
lds=Vector{Vector{Function}}([[ensemble_display]])

#perform GMC-NS steps until the ensemble is converged
converge_ensemble!(e,backup=(true,100),upper_displays=uds,lower_displays=lds, disp_rot_its=1000, converge_factor=1e-6)

Output:

Model libraries

CMZNicheSims.jl: Small library of population- and cell-based simulators of D. rerio circumferential marginal zone retinal progenitor cells.

Documentation

More extensive documentation is available here.