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Gregory Ashton
PyFstat
Commits
27e12115
Commit
27e12115
authored
Oct 22, 2016
by
Gregory Ashton
Browse files
Updates docs fixing errors in fc on glitching data
parent
115bcbac
Changes
5
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Inline
Sidebyside
docs/fully_coherent_search_using_MCMC_on_glitching_data.md
View file @
27e12115
...
...
@@ 5,14 +5,11 @@ search using MCMC](fully_coherent_search_using_MCMC.md), to the glitching signal
[
make fake data
](
make_fake_data.md]
)
. The aim here is to illustrate the effect
such a signal can have on a fullycoherent search. The complete script for this
example canbe found
[
here
](
../example/fully_cohrent_search_on_glitching_data.py
)
.
[
here
](
../example/fully_coh
e
rent_search_
using_MCMC_
on_glitching_data.py
)
.
We use the same prior as in the basic fullycoherent search, except that we
will modify the prior on
`F0`
to a flat uniform prior. The reason for this is
to highlight the multimodal nature of the posterior which results from the
glitch (a normal prior centered on one of the modes will bias one mode over
the other). So our initial set up is
After importing
`pyfstat`
, We setup a flat prior on
`F0`
and
`F1`
, based on the
values used to generate the signal:
```
from pyfstat import MCMCSearch
...
...
@@ 26,53 +23,57 @@ tref = 362750407.0
tstart = 1000000000
duration = 100*86400
tend = tstart
=
duration
tend = tstart
+
duration
theta_prior = {'F0': {'type': 'unif', 'lower': F05e5,
'upper': F0+5e5},
'F1': {'type': 'norm', 'loc': F1, 'scale': abs(1e6*F1)},
theta_prior = {'F0': {'type': 'unif', 'lower': F01e4, 'upper': F0+1e4},
'F1': {'type': 'unif', 'lower': F1*(1+1e3), 'upper': F1*(11e3)},
'F2': F2,
'Alpha': Alpha,
'Delta': Delta
}
```
Next, we will use 10 temperatures and a larger number of walkers  these have
been tuned to illustrate the bimodal nature of the posterior
In this search, we will use paralllel tempering (to help the walkers move
between the different peaks in the posterior).
```
ntemps =
10
betas = np.logspace(0, 30, ntemps)
nwalkers =
5
00
nsteps = [
1
00, 100
, 1
00]
ntemps =
2
log10temperature_min = 0.01
nwalkers =
1
00
nsteps = [
50
00, 10000]
mcmc = MCMCSearch('fully_coherent_on_glitching_data', 'data',
mcmc = MCMCSearch('fully_coherent_
search_using_MCMC_
on_glitching_data', 'data',
sftfilepath='data/*_glitch*.sft',
theta_prior=theta_prior, tref=tref, tstart=tstart, tend=tend,
nsteps=nsteps, nwalkers=nwalkers, ntemps=ntemps,
log10temperature_min=log10temperature_min
, scatter_val=1e6
)
log10temperature_min=log10temperature_min)
mcmc.run()
mcmc.plot_corner(add_prior=True)
```
Running this takes slightly longer than the basic example (a few minutes) and
produces a multimodal posterior:
![](
img/fully_coherent_on_glitching_data_corner.png
)
Running this example, we obtain traces of the walkers like this:
![](
img/fully_coherent_search_using_MCMC_on_glitching_data_walkers.png
)
Clearly one central peak pertains to the original frequency
`F0=30`
. At
`30+0.4e5`
, we find the second largest peak  this is the mode corresponding
to the second half of the data. In reality, we would expect both peaks to be
of equal size since the glitch occurs exactly half way through (see
[
how the
data was made
](
make_fake_data.md
)
). We will confirm this later on by performing
a grid search.
Although it is not obvious at first, the large widths of these traces in fact
show that the walkers are jumping between two bimodal peaks (for both
`F0`
and
`F1): this is possible due to the tuning of the parallel tempering. To see this
clearly, we also plot the corner plot:
![](img/fully_coherent_search_using_MCMC_on_glitching_data_corner.png)
Finally, the maximum twoF value found is
From this corner plot, we that unlike the in the [single glitch fullycoherent
search](full_coherent_search_using_MCMC.md), the posterior, even after a large
number of steps, is multimodal. However, these two peaks do **not** correspond
exactly to the two frequencies before and after the glitch, which would be
`
30
` and `
30+4e5
` (to see this, see how the data is
[generated](../examples/make_dake_data.py)). This is partly due to the noise
and partly due to the fact that the maximum detection statistic in the case
of glitches can occur at point *in between* the two frequencies. Moreover, we
see bimodality in `
F1
`, which did does not change during the glitch.
```
>>> mcmc.print_summary()
Max twoF:
411.595
Max twoF:
1354.7
```
That is, compared to the basic search (on a smooth signal) which had a twoF of
`17
56.4417724
6`
(in agreement with the predicted twoF), we have lost a large
`
~
176
4
`
(in agreement with the predicted twoF), we have lost a large
fraction of the SNR due to the glitch.
docs/img/fully_coherent_search_using_MCMC_on_glitching_data_corner.png
0 → 100644
View file @
27e12115
115 KB
docs/img/fully_coherent_search_using_MCMC_on_glitching_data_walkers.png
0 → 100644
View file @
27e12115
50.9 KB
examples/fully_coherent_search_using_MCMC_on_glitching_data.py
View file @
27e12115
...
...
@@ 18,10 +18,10 @@ theta_prior = {'F0': {'type': 'unif', 'lower': F01e4, 'upper': F0+1e4},
'Delta'
:
Delta
}
ntemps
=
10
log10temperature_min
=

3
0
nwalkers
=
5
00
nsteps
=
[
1
00
,
100
,
1
00
]
ntemps
=
2
log10temperature_min
=

0
.01
nwalkers
=
1
00
nsteps
=
[
50
00
,
10000
]
mcmc
=
MCMCSearch
(
'fully_coherent_search_using_MCMC_on_glitching_data'
,
'data'
,
sftfilepath
=
'data/*_glitch*.sft'
,
...
...
examples/make_fake_data.py
View file @
27e12115
...
...
@@ 24,7 +24,9 @@ data = Writer(
F2
=
F2
,
duration
=
duration
,
Alpha
=
Alpha
,
Delta
=
Delta
,
h0
=
h0
,
sqrtSX
=
sqrtSX
)
data
.
make_data
()
print
'Predicted fstat value:'
,
data
.
predict_fstat
()
# The predicted twoF, given by lalapps_predictFstat can be accessed by
twoF
=
data
.
predict_fstat
()
print
'Predicted twoF value: {}
\n
'
.
format
(
twoF
)
# Next, taking the same signal parameters, we include a glitch half way through
dtglitch
=
duration
/
2.0
...
...
@@ 37,11 +39,6 @@ glitch_data = Writer(
dtglitch
=
dtglitch
,
delta_F0
=
delta_F0
,
delta_F1
=
delta_F1
,
detector
=
'L1'
)
glitch_data
.
make_data
()
# The predicted twoF, given by lalapps_predictFstat can be accessed by
print
'Predicted fstat value:'
,
data
.
predict_fstat
()
# Making data with two glitches
dtglitch
=
[
duration
/
4.0
,
4
*
duration
/
5.0
]
...
...
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