MCMC search: Semicoherent F-statistic with initialisation

Directed MCMC search for an isolated CW signal using the fully-coherent F-statistic. Prior to the burn-in stage, walkers are initialized with a certain scattering factor.

 import pyfstat
 import numpy as np
 import os

 label = "PyFstat_example_MCMC_search_using_initialisation"
 outdir = os.path.join("PyFstat_example_data", label)

 # Properties of the GW data
 data_parameters = {
     "sqrtSX": 1e-23,
     "tstart": 1000000000,
     "duration": 100 * 86400,
     "detectors": "H1",
 }
 tend = data_parameters["tstart"] + data_parameters["duration"]
 mid_time = 0.5 * (data_parameters["tstart"] + tend)

 # Properties of the signal
 depth = 10
 signal_parameters = {
     "F0": 30.0,
     "F1": -1e-10,
     "F2": 0,
     "Alpha": np.radians(83.6292),
     "Delta": np.radians(22.0144),
     "tref": mid_time,
     "h0": data_parameters["sqrtSX"] / depth,
     "cosi": 1.0,
 }

 data = pyfstat.Writer(
     label=label, outdir=outdir, **data_parameters, **signal_parameters
 )
 data.make_data()

 # The predicted twoF, given by lalapps_predictFstat can be accessed by
 twoF = data.predict_fstat()
 print("Predicted twoF value: {}\n".format(twoF))

 DeltaF0 = 1e-7
 DeltaF1 = 1e-13
 VF0 = (np.pi * data_parameters["duration"] * DeltaF0) ** 2 / 3.0
 VF1 = (np.pi * data_parameters["duration"] ** 2 * DeltaF1) ** 2 * 4 / 45.0
 print("\nV={:1.2e}, VF0={:1.2e}, VF1={:1.2e}\n".format(VF0 * VF1, VF0, VF1))

 theta_prior = {
     "F0": {
         "type": "unif",
         "lower": signal_parameters["F0"] - DeltaF0 / 2.0,
         "upper": signal_parameters["F0"] + DeltaF0 / 2.0,
     },
     "F1": {
         "type": "unif",
         "lower": signal_parameters["F1"] - DeltaF1 / 2.0,
         "upper": signal_parameters["F1"] + DeltaF1 / 2.0,
     },
 }
 for key in "F2", "Alpha", "Delta":
     theta_prior[key] = signal_parameters[key]

 ntemps = 1
 log10beta_min = -1
 nwalkers = 100
 nsteps = [100, 100]

 mcmc = pyfstat.MCMCSearch(
     label=label,
     outdir=outdir,
     sftfilepattern=os.path.join(outdir, "*{}*sft".format(label)),
     theta_prior=theta_prior,
     tref=mid_time,
     minStartTime=data_parameters["tstart"],
     maxStartTime=tend,
     nsteps=nsteps,
     nwalkers=nwalkers,
     ntemps=ntemps,
     log10beta_min=log10beta_min,
 )
 mcmc.setup_initialisation(100, scatter_val=1e-10)
 mcmc.run(
     walker_plot_args={"plot_det_stat": True, "injection_parameters": signal_parameters}
 )
 mcmc.print_summary()
 mcmc.plot_corner(add_prior=True, truths=signal_parameters)
 mcmc.plot_prior_posterior(injection_parameters=signal_parameters)