Piecewise Polytropic Prior with ADM Example

The main purpose of this code is to demonstrate how one can fix the prior-likelihood to a constant value and use multinest to sample the prior space log-uniformly with asymmetric dark matter(ADM) present. Within this script, one can use the PosteriorAnalysis.pyscript to generate the prior axuiliary data and the prior 95% confidence intervals.

The following block of code will properly import NEoST and its prerequisites, furthermore it also defines a name for the inference run, this name is what will be prefixed to all of NEoST’s output files.

The machinary used within this script and the explanation of them is identical to those found in the Piecewise Polytropic, Speed of Sound, and Tabulated Examples.

import neost
from neost.eos import polytropes
from neost.Prior import Prior
from neost.Star import Star
from neost.Likelihood import Likelihood
from neost import PosteriorAnalysis
from scipy.stats import multivariate_normal
from scipy.stats import gaussian_kde
import numpy as np
import matplotlib
from matplotlib import pyplot as plt
from pymultinest.solve import solve
import time
import os
if not os.path.exists("chains"):
   os.mkdir("chains")

import neost.global_imports as global_imports

# Some physical constants
c = global_imports._c
G = global_imports._G
Msun = global_imports._M_s
pi = global_imports._pi
rho_ns = global_imports._rhons

Below, we define the piecewise polytripic equation of state model, import the J0740 likelihood function, set the ADM particle type to be a boson, and set whether we want to calculate ADM halos as well as the two-fluid tidal deformability. Note, both dm_halo and two_fluid_tidal are set to be False by default, so a user doesn’t need to define them before-hand if they don’t want to consider them in their inference. We wanted to highlight these parameters so that one knew where to define them in the event that either parameter were to be considered.

# Define name for run
run_name = "prior-hebeler-pp-bosonic-adm-"

# We're exploring a polytropic (P) EoS parametrization with a chiral effective field theory (CEFT) parametrization based on Hebeler's work
# Transition between CS parametrisation and CEFT parametrization occurs at 1.1*saturation density
polytropes_pp = polytropes.PolytropicEoS(crust = 'ceft-Hebeler', rho_t = 1.1*rho_ns, adm_type = 'Bosonic',dm_halo = False,two_fluid_tidal = False)

Below, we define the piecewise polytripic equation of state model, import the J0740 likelihood function, and set the variable paramaeters with their respective prior space intervals depending on the their adm_type string parameter value. This is because the ADM priors are dependent on if one specifies that it is a boson or fermion.

# Create the likelihoods for the individual measurements
mass_radius_j0740 = np.load('j0740.npy').T
J0740_LL = gaussian_kde(mass_radius_j0740)

# Pass the likelihoods to the solver
likelihood_functions = [J0740_LL.pdf]
likelihood_params = [['Mass', 'Radius']]

# Define whether event is GW or not and define number of stars/events
chirp_mass = [None]
number_stars = len(chirp_mass)

# Define variable parameters, same prior as previous papers of Raaijmakers et al

print(polytropes_pp.adm_type)
if polytropes_pp.adm_type == 'Bosonic':
    variable_params={'ceft':[polytropes_pp.min_norm, polytropes_pp.max_norm],'gamma1':[1.,4.5],'gamma2':[0.,8.],'gamma3':[0.5,8.],'rho_t1':[1.5,8.3],'rho_t2':[1.5,8.3],
                    'mchi':[-2, 8],'gchi_over_mphi': [-3,3],'adm_fraction':[0., 5.]}
elif polytropes_pp.adm_type == 'Fermionic':
    variable_params={'ceft':[polytropes_pp.min_norm, polytropes_pp.max_norm],'gamma1':[1.,4.5],'gamma2':[0.,8.],'gamma3':[0.5,8.],'rho_t1':[1.5,8.3],'rho_t2':[1.5,8.3],
                    'mchi':[-2, 9],'gchi_over_mphi': [-5,3],'adm_fraction':[0., 1.7]}

if polytropes_pp.adm_type == 'None':
    variable_params={'ceft':[polytropes_pp.min_norm, polytropes_pp.max_norm],'gamma1':[1.,4.5],'gamma2':[0.,8.],'gamma3':[0.5,8.],'rho_t1':[1.5,8.3],'rho_t2':[1.5,8.3]}

#Note if the user wants to have a seperate adm_fraction per source, include it below via
#'adm_fraction_' + str(i+1):[0., 5.]. And eliminate the adm_fraction above, as that is to assume all Neutron stars have the same amount of adm_fraction
for i in range(number_stars):
    variable_params.update({'rhoc_' + str(i+1):[14.6, 16]})

# Define static parameters, empty dict because all params are variable
static_params={}

Bosonic

Finally, the prior object must be created using the following function call:neost.Prior.Prior(EOS, variable_params, static_params, chirp_masses) where the EOS argument is the equation of state object that was created in the previous step. When this prior is called it will then uniformly sample sets of parameters from the defined parameter ranges.

The likelihood is defined by providing both the previously defined prior object and the likelihood functions defined in the previous codeblock. This is done with the following code: likelihood = Likelihood(prior, likelihood_functions, likelihood_params, chirp_mass)

# Define prior
prior = Prior(polytropes_pp, variable_params, static_params, chirp_mass)
likelihood = Likelihood(prior, likelihood_functions, likelihood_params, chirp_mass)

print("Bounds of prior are")
print(variable_params)
print("number of parameters is %d" %len(variable_params))

Bounds of prior are
{'ceft': [1.676, 2.814], 'gamma1': [1.0, 4.5], 'gamma2': [0.0, 8.0], 'gamma3': [0.5, 8.0], 'rho_t1': [1.5, 8.3], 'rho_t2': [1.5, 8.3], 'mchi': [-2, 8], 'gchi_over_mphi': [-3, 3], 'adm_fraction': [0.0, 5.0], 'rhoc_1': [14.6, 16]}
number of parameters is 10

When finished with testing your likelihood and prior you can proceed to the actual inference process. This is done in the code block below. Warning: depending on the performance of your platform, this might be a very slow process. To make it slightly faster, we have decreased the number of live points and set a maximum number of iterations for this example. For a proper analysis, we would remove the max_iter argument and set, for example, n_live_points=30000.

# Then we start the sampling, note the greatly increased number of livepoints, this is required because each livepoint terminates after 1 iteration
start = time.time()
result = solve(LogLikelihood=likelihood.loglike_prior, Prior=prior.inverse_sample, n_live_points=100, evidence_tolerance=0.1,
               n_dims=len(variable_params), sampling_efficiency=0.8, outputfiles_basename='chains/' + run_name, verbose=True, resume = True)
end = time.time()
print(end - start)

 MultiNest Warning: no resume file found, starting from scratch
 *****************************************************
 MultiNest v3.10
 Copyright Farhan Feroz & Mike Hobson
 Release Jul 2015

 no. of live points =  100
 dimensionality =   10
 *****************************************************
 Starting MultiNest
 generating live points
 live points generated, starting sampling
Acceptance Rate:                        1.000000
Replacements:                                100
Total Samples:                               100
Nested Sampling ln(Z):            **************
Importance Nested Sampling ln(Z):       1.000000 +/-       NaN
  analysing data from chains/prior-hebeler-pp-bosonic-adm-.txt
 ln(ev)=   1.0000000000000004      +/-                       NaN
 Total Likelihood Evaluations:          100
 Sampling finished. Exiting MultiNest
171.8531928062439

PosteriorAnalysis.compute_prior_auxiliary_data('chains/' + run_name, polytropes_pp,
                                        variable_params, static_params,dm = True)

Total number of samples is 100
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sample too small for 65959462574187320.00
sample too small for 70370325234111880.00
sample too small for 75076152538158464.00
sample too small for 80096669458060016.00
sample too small for 85452920020282384.00
sample too small for 91167355514279856.00
sample too small for 97263928599448880.00
sample too small for 103768193705221808.00
sample too small for 110707414145159728.00
sample too small for 118110676394006288.00
sample too small for 126009012006712816.00
sample too small for 134435527690482288.00
sample too small for 143425544075018160.00
sample too small for 153016743762678304.00
sample too small for 163249329279076576.00
sample too small for 174166191586206816.00
sample too small for 185813089864445728.00
sample too small for 198238843316974976.00
sample too small for 211495535800633248.00
sample too small for 225638734140894144.00
sample too small for 240727721046073568.00
sample too small for 256825743597069824.00
sample too small for 274000278354162368.00
sample too small for 292323314192148736.00
sample too small for 311871654049304192.00
sample too small for 332727236854994624.00
sample too small for 354977480985363136.00
sample too small for 378715650686657216.00
sample too small for 404041247002178240.00
sample too small for 431060424841397056.00
sample too small for 459886437939447360.00
sample too small for 490640113572132928.00
sample too small for 523450359016174848.00
sample too small for 558454701877691840.00
sample too small for 595799866553663360.00
sample too small for 635642389242707968.00
sample too small for 678149274083111552.00
sample too small for 723498693168256384.00
sample too small for 771880733373789056.00
sample too small for 823498193126804352.00
sample too small for 878567432456831488.00
sample too small for 937319279891776640.00
sample too small for 1000000000000000000.00

PosteriorAnalysis.cornerplot('chains/' + run_name, variable_params, dm = True)

PosteriorAnalysis.mass_radius_prior_predictive_plot('chains/' + run_name,variable_params, label_name='+ J0740 dataset')