Tutorials

A Bayesian analysis of a gravitational-wave signal which is not accompanied by electromagnetic signals can be performed within nmma following two main steps:

1) setting up a config.ini file and running the command

nmma_gw_generation config.ini

2) perform the analysis or parameter estimation using:

nmma_gw_analysis <name_of_analysis>_data_dump.pickle

Below, we provide an example of a gravitational-wave inference setup using observational data of GW170817 and another example for an injection based analysis.

1) We start to set up a config.ini file and adapt it to our specific case. An example is shown below:

################################################################################
## Data generation arguments
################################################################################

trigger_time = 1187008882.43

################################################################################
## Detector arguments
################################################################################

detectors = [H1, L1, V1]
psd_dict = {H1=data/GW170817/h1_psd.txt, L1=data/GW170817/l1_psd.txt, V1=data/GW170817/v1_psd.txt}
channel_dict = {H1=LOSC-STRAIN, L1=LOSC-STRAIN, V1=LOSC-STRAIN}
 data_dict = {H1=data/GW170817/H-H1_LOSC_CLN_16_V1-1187007040-2048.gwf, L1=data/GW170817/L- 
 L1_LOSC_CLN_16_V1-1187007040-2048.gwf, V1=data/GW170817/V-V1_LOSC_CLN_16_V1-1187007040-2048.gwf}
 duration = 128

################################################################################
## Job submission arguments
################################################################################

label = GW170817
outdir = outdir

################################################################################
## Likelihood arguments
################################################################################

distance-marginalization=False
phase-marginalization=False
time-marginalization=False

################################################################################
## Prior arguments
################################################################################

prior-file = GW170817.prior

################################################################################
## Waveform arguments
################################################################################

frequency-domain-source-model = lal_binary_neutron_star
waveform_approximant = IMRPhenomPv2_NRTidalv2
binary-type=BNS

################################################################################
## EOS arguments
################################################################################

with-eos=True 
eos-data=./eos/eos_sorted 
Neos=x<provide_number_EOS_files>
eos-weight=./eos/EOS_sorted_weight.dat

The trigger time is the time of the observed event. With regard to detector arguments, one has to specify which detectors should be used. For example, detectors = [H1, L1, V1] stand for LIGO detectors Hanford, Livingston and Virgo. For each detector, the noise power spectral density of gravitational wave detector needs to be provided. Within data_dict, one needs to provide the GW170817 data measured within each detector.

With regard to likelihood arguments, we can specify if want a marginal likelihood that has been integrated over the parameter space, e.g. for distance, phase, or time. The prior file should be tailored to the observed event, in this case GW170817 but also with regard to the GW model that is used for the parameter estimation. The GW model can be specified in waveform_approximant. Here, we use the phenomenological model IMRPhenomPv2_NRTidalv2 for a precessing binary neutron star model.

For inferring the source properties of GW170817, we will sample over a set of EOSs that were computed with Chiral Effective Field Theory. The EOS set 15nsat_cse_natural_R14 was used in the study of Huth et al. and can be downloaded there. In order to make use of the EOS set during the sampling, a pre-routine is required. Within this step, one can include different constraints on the NS EOS such as measurement of NICER or pulsar measurements which is reflected in the EOS_sorted_weight.dat and one needs to sort the EOS files eos_sorted in order to reduce sampling time.

Once the config.ini file is set, the generation can be run with nmma_gw_generation config.ini which will create a directory outdir. The submit file for the inference can be found under outdir/data/<name_of_analysis>_data_dump.pickle in the example above it would be GW170817_data_dump.pickle. For the analysis of GW signals, it is recommended to run the inference (nmma_gw_analysis <name_of_analysis>_data_dump.pickle) on larger clusters. An exemplary submit script is shown below:

#!/bin/bash
#SBATCH -p <queue_name>
#SBATCH --job-name=GW170817
#SBATCH --nodes=17
#SBATCH --ntasks-per-node=48
#SBATCH --time=48:00:00
#SBATCH -o outdir/log_data_analysis/GW170817.log
#SBATCH -e outdir/log_data_analysis/GW170817.err
#SBATCH -D ./
#SBATCH --export=NONE
#SBATCH --no-requeue
#SBATCH --account=<account_name>
#SBATCH --mail-type=BEGIN,END
#SBATCH --mail-user=<email>
      
module load slurm_setup
module load python/3.8
source <path_to_environment>/bin/activate
      
export SLURM_EAR_LOAD_MPI_VERSION="intel"    #for Intel MPI
export MKL_NUM_THREADS="1"
export MKL_DYNAMIC="FALSE"
export OMP_NUM_THREADS=1
export MPI_PER_NODE=48
      
mpiexec -n $SLURM_NTASKS nmma_gw_analysis outdir/data/GW170817_data_dump.pickle --nlive 2048 --maxmcmc 10000 --nact 10 --no-plot --label GW170817 --outdir outdir/result --sampling-seed 1234

The final posterior samples for the observed event GW170817 can be found under outdir/result/.

For synthetic signals, the `config.ini` file needs to be slightly adapted. First of all, some injection specific flags need to be provided which are listed below:

################################################################################
## Injection arguments
################################################################################

injection = True
n-simulation = 1
injection-file = ./injections.json
injection_numbers=[0]

The injection = True flag enables parameter estimation with injected signals and n-simulation = 1 initiates inference for one synthetic signal. An injection-file needs to be provided in order to specify for which system the inference should be run. The creation of injected signals is shown here. The injection_numbers= [0] uses in this case only the first signal in the injection file.

Moreover, other flags which are related to an observed event should be commented out such as trigger time and provided observational data. The rest remains the same as shown above for the case of an observed GW event.