Commit ed1b32c1 authored by Gregory Ashton's avatar Gregory Ashton
Browse files

Adds volume convergence investigation

parent 65b75b77
. /home/gregory.ashton/lalsuite-install/etc/
export PATH="/home/gregory.ashton/anaconda2/bin:$PATH"
export MPLCONFIGDIR=/home/gregory.ashton/.config/matplotlib
for ((n=0;n<1;n++))
/home/gregory.ashton/anaconda2/bin/python "$1" /local/user/gregory.ashton --no-template-counting --no-interactive
mv /local/user/gregory.ashton/VolumeConvergenceResults_"$1".txt $(pwd)/CollectedOutput
import pyfstat
import numpy as np
import os
import sys
import time
ID = sys.argv[1]
outdir = sys.argv[2]
label = 'VCrun_{}'.format(ID)
data_label = 'VCrunData_{}_'.format(ID)
results_file_name = '{}/VolumeConvergenceResults_{}.txt'.format(outdir, ID)
# Properties of the GW data
sqrtSX = 1e-23
tstart = 1000000000
Tspan = 100*86400
tend = tstart + Tspan
# Fixed properties of the signal
F0 = 30
F1 = -1e-10
F2 = 0
Alpha = np.radians(83.6292)
Delta = np.radians(22.0144)
tref = .5*(tstart+tend)
depth = 100
h0 = sqrtSX / float(depth)
psi = np.random.uniform(-np.pi/4, np.pi/4)
phi = np.random.uniform(0, 2*np.pi)
cosi = np.random.uniform(-1, 1)
data = pyfstat.Writer(
label=data_label, outdir=outdir, tref=tref,
tstart=tstart, F0=F0, F1=F1, F2=F2, duration=Tspan, Alpha=Alpha,
Delta=Delta, h0=h0, sqrtSX=sqrtSX, psi=psi, phi=phi, cosi=cosi,
twoF_PM = data.predict_fstat()
nsteps = [500, 500]
Vs = np.arange(50, 550, 50)
Vs = [50, 150, 200, 250, 350, 400, 450]
for V in Vs:
DeltaF0 = V * np.sqrt(3)/(np.pi*Tspan)
DeltaF1 = V * np.sqrt(45/4.)/(np.pi*Tspan**2)
startTime = time.time()
theta_prior = {'F0': {'type': 'unif',
'lower': F0-DeltaF0/2.0,
'upper': F0+DeltaF0/2.0},
'F1': {'type': 'unif',
'lower': F1-DeltaF1/2.0,
'upper': F1+DeltaF1/2.0},
'F2': F2,
'Alpha': Alpha,
'Delta': Delta
ntemps = 3
log10temperature_min = -0.5
nwalkers = 100
mcmc = pyfstat.MCMCSearch(
label=label, outdir=outdir, nsteps=nsteps,
sftfilepath='{}/*{}*sft'.format(outdir, data_label),
tref=tref, minStartTime=tstart, maxStartTime=tend,
nwalkers=nwalkers, ntemps=ntemps,
convergence_period=10, convergence_length=10,
convergence_burnin_fraction=0.1, convergence_threshold_number=5,
convergence_threshold=1.1, convergence_early_stopping=False),
log_table=False, gen_tex_table=False
cdF0, cdF1 = mcmc.convergence_diagnostic[-1]
d, maxtwoF = mcmc.get_max_twoF()
d_med_std = mcmc.get_median_stds()
dF0 = F0 - d['F0']
dF1 = F1 - d['F1']
F0_std = d_med_std['F0_std']
F1_std = d_med_std['F1_std']
runTime = time.time() - startTime
with open(results_file_name, 'a') as f:
f.write('{} {:1.8e} {:1.8e} {:1.8e} {:1.8e} {:1.8e} {:1.8e} {:1.8e} {:1.8e} {:1.5e} {:1.5e} {}\n'
.format(V, dF0, dF1, F0_std, F1_std, DeltaF0, DeltaF1, maxtwoF, twoF_PM, cdF0, cdF1,
os.system('rm {}/*{}*'.format(outdir, label))
os.system('rm {}/*{}*'.format(outdir, data_label))
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
import os
from tqdm import tqdm
from oct2py import octave
import glob
import scipy.stats
filenames = glob.glob("CollectedOutput/*.txt")'paper')
Tspan = 100 * 86400
df_list = []
for fn in filenames:
if '3356003' in fn:
df = pd.read_csv(
fn, sep=' ', names=['V', 'dF0', 'dF1', 'F0_std', 'F1_std', 'DeltaF0',
'DeltaF1', 'MaxtwoF', 'twoF_PM', 'cdF0', 'cdF1', 'runTime'])
df['mismatch'] = (df.twoF_PM - df.MaxtwoF)/df.twoF_PM
df['F0_fraction'] = df.F0_std / df.DeltaF0
df['F1_fraction'] = df.F1_std / df.DeltaF1
df['CLUSTER_ID'] = fn.split('_')[1]
df['RUN_ID'] = fn.split('_')[2]
df = pd.concat(df_list)
df.sort_values('V', inplace=True)
df['cd_ave'] = df[['cdF0', 'cdF1']].mean(axis=1)
df['fraction_ave'] = df[['F0_fraction', 'F1_fraction']].mean(axis=1)
df = df[df.V <= 500]
fig, (ax2, ax3) = plt.subplots(nrows=2, figsize=(3.2, 4), sharex=True)
print df.groupby('V')['dF0'].count()
Vs = df['V'].unique()
mismatch_ave = df.groupby('V')['mismatch'].mean()
ave_cd_ave = df.groupby('V')['cd_ave'].apply(scipy.stats.mstats.gmean)
cdF0_ave = df.groupby('V')['cdF0'].mean()
cdF1_ave = df.groupby('V')['cdF1'].mean()
ave_fraction_ave = df.groupby('V')['fraction_ave'].median()
F0_fraction_ave = df.groupby('V')['F0_fraction'].mean()
F1_fraction_ave = df.groupby('V')['F1_fraction'].mean()
ax2.plot(df.V, df.cd_ave, 'o', color='k', alpha=0.5)
#ax2.plot(Vs, ave_cd_ave, color='r')
ax2.set_ylim(0, 10)
ax2.set_ylabel(r'$\langle \textrm{PSRF} \rangle$')
ax3.plot(df.V, df.fraction_ave, 'o', color='k', alpha=0.2)
#ax3.plot(Vs, ave_fraction_ave, color='r')
ax3.set_ylabel(r'$\langle \textrm{posterior std. / prior width} \rangle$')
ax3.set_xlim(0, 525)
request_cpus = 1
request_memory = 16 GB
Queue 100
......@@ -32,4 +32,5 @@
......@@ -888,6 +888,61 @@ chains remain isolated from the main bulk can be easily countered by the use
of parallel tempering (see Sec.~\ref{sec_parallel_tempering}). This was intenionally
not used here to highlight the utility of the convergence statistic.
\section{Choice of the prior metric volume}
The prior volume estimates the approximate size of the parameter space relative
to the size of a signal; any optimization routine, given finite resources,
will fail if this volume is too large. We will now investigate precisely what
this means for an MCMC search given a fixed search setup.
In a data set of 100 days, we simulate Gaussian noise and a signal with a
sensitivity depth of 100. Then, we perform a directed search (over $f$ and
$\fdot$) with 500 burn-in and 500 production steps, 100 walkers, and using
parallel tempering with $\Ntemps=3, \logmintemp=-3$. The prior for the search
is uniform in frequency and spin-down with the width defined by an equal and
fixed metric volume (i.e. $\Vpe^{(0)}=\Vpe^{(1)}$). This process is repeated
500 times for a range of prior volumes so that we can infer the statistical
behaviour. In the upper panel of Fig.~\ref{fig_volume_convergence} we plot the
PSRF (calculated for a subset of the production samples) averaged over the two
search dimensions fo each simulation; this demonstrates that for $\sqrt{\V}
\gtrsim 200$, the majority of simulations where not converged (i.e. having
PSRF < 1.2). For $\sqrt{\V}=100$, only one simulation of the 500 failed, while
for $\sqrt{V}=50$ all simulations reached convergence.
\caption{Results of a study into the convergence of MCMC simulations as a
function of the prior volume}
It is reasonable to ask ``what happens for these cases that don't converge?''.
For all the simulations considered here, the MCMC algorithim did find the peak
in the likelhood: this was demonstrated by checking that the minimum mismatch
for each simulation was $\lesssim 0.1$. However, for those simulations which
where not converged, this was true only for a small subset of the walkers, the
other walkers where sampling other points in the parameter space (away from the
signal) and hence had not converged. This is demonstrated in the lower panel of
Fig.~\ref{fig_volume_convergence} where we plot the ratio of the posterior
standard deviation to the prior width (averaged over the two search
dimensions). For the converged solutions, this is small indicating that the
posterior is narrower than the prior. However, for the solution which did not
converge, this ratio is larger; if none of the walkers had converged and hence
the posterior samples where equivalent to the prior (i.e. uniform over some
range), we would expect this ratio to be $\sim 0.29$. For the largest prior
volumes considered here the ratio approaches this value.
This equivalence of the posterior to the prior is expected behaviour since the
walkers are initialised from the uniform prior (which is much wider than the
signal); if we had extended the burn-in period, we would expect eventually for
these walkers to converge: the performance at a fixed prior volume will depend
on the setup.
For a given setup, one can choose the optimal prior volume (i.e. balancing the
risk of loosing the signal due to non-convergence against computing cost) by
stipulating a failure rate; for this example one may choose $\sqrt{\V}=100$ based
on an estimated failure rate of 1 in 500.
\section{Zoom follow-up}
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