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Gregory Ashton
PyFstat
Commits
653149ea
Commit
653149ea
authored
Dec 21, 2016
by
Gregory Ashton
Browse files
Update to examples and adds new macros
parent
f2379bbd
Changes
4
Hide whitespace changes
Inline
Side-by-side
Paper/Examples/fully_coherent_search_using_MCMC.py
View file @
653149ea
...
...
@@ -59,3 +59,18 @@ mcmc = pyfstat.MCMCSearch(
mcmc
.
run
(
context
=
'paper'
,
subtractions
=
[
30
,
-
1e-10
])
mcmc
.
plot_corner
(
add_prior
=
True
)
mcmc
.
print_summary
()
from
latex_macro_generator
import
write_to_macro
write_to_macro
(
'BasicExampleF0'
,
'{:1.0f}'
.
format
(
F0
),
'../macros.tex'
)
write_to_macro
(
'BasicExampleF1'
,
F1
,
'../macros.tex'
)
write_to_macro
(
'BasicExampleh0'
,
h0
,
'../macros.tex'
)
write_to_macro
(
'BasicExampleSqrtSn'
,
sqrtSX
,
'../macros.tex'
)
write_to_macro
(
'BasicExampleDepth'
,
depth
,
'../macros.tex'
)
write_to_macro
(
'BasicExampleDeltaF0'
,
DeltaF0
,
'../macros.tex'
)
write_to_macro
(
'BasicExampleDeltaF1'
,
DeltaF1
,
'../macros.tex'
)
write_to_macro
(
'BasicExampleVF0'
,
VF0
,
'../macros.tex'
)
write_to_macro
(
'BasicExampleVF1'
,
VF1
,
'../macros.tex'
)
write_to_macro
(
'BasicExampleV'
,
VF0
*
VF1
,
'../macros.tex'
)
write_to_macro
(
'BasicExamplenburn'
,
nsteps
[
0
],
'../macros.tex'
)
write_to_macro
(
'BasicExamplenprod'
,
nsteps
[
1
],
'../macros.tex'
)
Paper/Examples/transient_search_using_MCMC.py
View file @
653149ea
...
...
@@ -16,7 +16,7 @@ data_tstart = tstart - duration
data_tend
=
data_tstart
+
3
*
duration
tref
=
.
5
*
(
data_tstart
+
data_tend
)
h0
=
1
e-2
3
h0
=
5
e-2
4
sqrtSX
=
1e-22
transient
=
pyfstat
.
Writer
(
...
...
@@ -26,9 +26,7 @@ transient = pyfstat.Writer(
transient
.
make_data
()
print
transient
.
predict_fstat
()
DeltaF0
=
6e-7
DeltaF0
=
1e-7
DeltaF1
=
1e-13
VF0
=
(
np
.
pi
*
duration
*
DeltaF0
)
**
2
/
3.0
VF1
=
(
np
.
pi
*
duration
**
2
*
DeltaF1
)
**
2
*
4
/
45.
...
...
@@ -48,7 +46,7 @@ theta_prior = {'F0': {'type': 'unif',
ntemps
=
3
log10temperature_min
=
-
1
nwalkers
=
100
nsteps
=
[
75
0
,
25
0
]
nsteps
=
[
10
0
,
10
0
]
mcmc
=
pyfstat
.
MCMCSearch
(
label
=
'transient_search_initial_stage'
,
outdir
=
'data'
,
...
...
Paper/macros.tex
View file @
653149ea
\def\DirectedMCNoiseOnlyMaximum
{
52.4
}
\def\DirectedMCNoiseN
{
10000
}
\def\AllSkyMCNoiseOnlyMaximum
{
59.8
}
\def\AllSkyMCNoiseN
{
10000
}
\def\AllSkyMCNoiseOnlyMaximum
{
59.8
}
\def\BasicExampleDeltaFone
{
1.0
{
\times
}
10
^{
-13
}}
\def\BasicExampleDeltaFzero
{
1.0
{
\times
}
10
^{
-7
}}
\def\BasicExampleDepth
{
10.0
}
\def\BasicExampleFone
{
-1.0
{
\times
}
10
^{
-10
}}
\def\BasicExampleFzero
{
30
}
\def\BasicExampleSqrtSn
{
1.0
{
\times
}
10
^{
-23
}}
\def\BasicExampleV
{
120.0
}
\def\BasicExampleVFone
{
49.0
}
\def\BasicExampleVFzero
{
2.5
}
\def\BasicExamplehzero
{
1.0
{
\times
}
10
^{
-24
}}
\def\BasicExamplenburn
{
50.0
}
\def\BasicExamplenprod
{
50.0
}
\def\DirectedMCNoiseN
{
10000
}
\def\DirectedMCNoiseOnlyMaximum
{
52.4
}
Paper/paper_cw_mcmc.tex
View file @
653149ea
...
...
@@ -672,11 +672,12 @@ metric-mismatch of unity.}
In order to familiarise the reader with the features of an MCMC search, we will
now describe a simple directed search (over
$
f
$
and
$
\dot
{
f
}$
) for a simulated
signal in Gaussian noise. The signal will have a frequency of
$
30
$
~Hz and a
spin-down of
$
-
1
{
\times
}
10
^{
-
10
}$
~Hz/s, all other Doppler parameters are
`known' and so are irrelevant. Moreover, the signal has an amplitude
$
h
_
0
=
10
^{
-
24
}$
~Hz
$^{
-
1
/
2
}$
while the Gaussian noise has
$
\Sn
=
10
^{
-
23
}$
~Hz
$^{
-
1
/
2
}$
such that the signal has a depth of 10.
signal in Gaussian noise. The signal will have a frequency of
$
\BasicExampleFzero
$
~Hz and a spin-down of
$
\BasicExampleFone
$
~Hz/s, all other
Doppler parameters are known and so are irrelevant. Moreover, the signal has an
amplitude
$
\BasicExamplehzero
$
~Hz
$^{
-
1
/
2
}$
while the Gaussian noise has
$
\sqrt
{
\Sn
}
=
\BasicExampleSqrtSn
$
~Hz
$^{
-
1
/
2
}$
such that the signal has a depth
of
$
\BasicExampleDepth
$
.
First, we must define a prior for each search parameter Typically, we recommend
either a uniform prior bounding the area of interest, or a normal distribution
...
...
@@ -684,23 +685,23 @@ centered on the target and with some well defined width. However, to ensure
that the MCMC simulation has a reasonable chance at finding a peak, one should
consider the corresponding metric-volume given in
Equation~
\eqref
{
eqn
_
metric
_
volume
}
. For this example, we will use a uniform
prior with a frequency range of
$
\Delta
f
=
10
^{
-
7
}$
~Hz and a spin-down range
of
$
\Delta
\fdot
=
10
^{
-
13
}
$
~Hz/s both centered on
the simulated signal frequency
and spin-down rate. We set the reference time to
coincide with the middle of
the data span, therefore the metric volume can be
decomposed into the frequency
contribution and spin-down contribution:
prior with a frequency range of
$
\Delta
f
=
\BasicExampleDeltaFzero
$
~Hz and a
spin-down range
of
$
\Delta
\fdot
=
\BasicExampleDeltaFone
$
~Hz/s both centered on
the simulated signal frequency
and spin-down rate. We set the reference time to
coincide with the middle of
the data span, therefore the metric volume can be
decomposed into the frequency
contribution and spin-down contribution:
frequency,
\begin{align}
\Vpe
^{
(0)
}
=
\frac
{
(
\pi\Tcoh\Delta
f)
^
2
}{
3
}
\approx
2.46
\Vpe
^{
(0)
}
=
\frac
{
(
\pi\Tcoh\Delta
f)
^
2
}{
3
}
\approx
\BasicExampleVFzero
\end{align}
and
\begin{align}
\Vpe
^{
(1)
}
=
\frac
{
4(
\pi\Delta
\fdot
)
^
2
\Tcoh
^{
4
}}{
45
}
\approx
48.9
\Vpe
^{
(1)
}
=
\frac
{
4(
\pi\Delta
\fdot
)
^
2
\Tcoh
^{
4
}}{
45
}
\approx
\BasicExampleVFone
\end{align}
such that
$
\V\approx
120
$
(note that
$
\Vsky
$
does not contribute
since we do
not search over the sky parameters). This metric volume indicates
that the
signal will occupy about 1
\%
of the prior volume, therefore the MCMC
is
expected to work. Alternative priors will need careful thought about how to
such that
$
\V\approx
\BasicExampleV
$
(note that
$
\Vsky
$
does not contribute
since we do
not search over the sky parameters). This metric volume indicates
that the
signal will occupy about 1
\%
of the prior volume, therefore the MCMC
is
expected to work. Alternative priors will need careful thought about how to
translate them into a metric volume: for example using a Gaussian one could use
the standard deviation as a proxy for the allowed search region.
...
...
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