quickstart.py

from numpy import pi, log
import pypolychord
from pypolychord.priors import UniformPrior
try:
    from mpi4py import MPI
except ImportError:
    pass


#| Define a four-dimensional spherical gaussian likelihood,
#| width sigma=0.1, centered on the 0 with one derived parameter.
#| The derived parameter is the squared radius

nDims = 4
nDerived = 1
sigma = 0.1

def likelihood(theta):
    """ Simple Gaussian Likelihood"""

    nDims = len(theta)
    r2 = sum(theta**2)
    logL = -log(2*pi*sigma*sigma)*nDims/2.0
    logL += -r2/2/sigma/sigma

    return logL, [r2]

#| Define a box uniform prior from -1 to 1

def prior(hypercube):
    """ Uniform prior from [-1,1]^D. """
    return UniformPrior(-1, 1)(hypercube)

#| Optional dumper function giving run-time read access to
#| the live points, dead points, weights and evidences

def dumper(live, dead, logweights, logZ, logZerr):
    print("Last dead point:", dead[-1])

#| Parameter names
#! This is a list of tuples (label, latex)
#! Derived parameters should be followed by a *

paramnames = [(f'p{i}', f'\\theta_{i}') for i in range(nDims)]
paramnames += [('r*', 'r')]

#| Run PolyChord

output = pypolychord.run(
    likelihood,
    nDims,
    nDerived=nDerived,
    prior=prior,
    dumper=dumper,
    file_root='gaussian',
    nlive=200,
    do_clustering=True,
    read_resume=False,
    paramnames=paramnames,
)

#| Make an anesthetic plot 

try:
    from anesthetic import make_2d_axes
    fig, ax = make_2d_axes(['p0', 'p1', 'p2', 'p3', 'r'])
    output.plot_2d(ax)
    fig.savefig('posterior.pdf')
except ImportError:
    print("Install anesthetic for plotting examples.")