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Multipole
Daniel edited this page May 19, 2017
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Generate a toy mock dataset from a distortion-free theory + noise sampled from a diagonal DR10 icov from Timothée. Binning is (rP,rT) with [0:200]*40 (5 Mpc/h bins). (The failed to estimate full covariance matrix error is because we only generate one MC sample, and is safe to ignore.)
./baofit -i ../config/comoving.ini --data rTPFullDiag --load-icov --output-prefix mock_ --rmin 0 --rmax 500 --toymc-samples 1 --toymc-save --no-initial-fit --ndump 0
mv mock_toymcsave.data mock.data
cp rTPFullDiag.icov mock.icov
Now do a cosmo fit to this toy mock with only beta, alpha-par and alpha-perp floating, and 40 <= r <= 180 Mpc/h:
./baofit -i ../config/comoving.ini --data mock --load-icov --dist-add "" --dist-mul "" --output-prefix mock_fit_
Fit results: chiSquare / dof = 953.019 / (963-3), prob = 0.557438, log(det(Covariance)) = -21069
FMIN Value = 476.509617 at:
beta = 1.415525 +/- 0.068162 $ 1.42 \pm 0.07 $
BAO alpha-parallel = 1.002008 +/- 0.018076 $ 1.002 \pm 0.018 $
BAO alpha-perp = 0.972253 +/- 0.028145 $ 0.972 \pm 0.028 $
FMIN Errors & Correlations =
beta : 0.068162
BAO alpha-parallel : -0.015233 0.018076
BAO alpha-perp : 0.027790 -0.413302 0.028145
Next, fit the same toy mock to find its best fit multipoles at r = 40,45,50,...,180 (29 points). First, we fit all multipoles (ell = 0,2,4) for a total of 3*29 = 87 params:
./baofit -i ../config/comoving_xi.ini --data mock --load-icov --output-prefix mock_ell024_ \
--xi-points 40,45,50,55,60,65,70,75,80,85,90,95,100,105,110,115,120,125,130,135,140,145,150,155,160,165,170,175,180
Fit results: chiSquare / dof = 847.708 / (963-87), prob = 0.74773, log(det(Covariance)) = -21069
Xi y-0-0 = 6.139316 +/- 0.697306 $ 6.1 \pm 0.7 $
Xi y-0-1 = 3.835945 +/- 0.418932 $ 3.8 \pm 0.4 $
Xi y-0-2 = 3.794558 +/- 0.391574 $ 3.8 \pm 0.4 $
...
For comparison, we also fit just the mono+quad (ell = 0,2) using model-config to fix the hexadecapole parameters to zero:
./baofit -i ../config/comoving_xi.ini --data mock --load-icov --output-prefix mock_ell02_ --model-config="fix[Xi y-4-*]=0" \
--xi-points 40,45,50,55,60,65,70,75,80,85,90,95,100,105,110,115,120,125,130,135,140,145,150,155,160,165,170,175,180
Fit results: chiSquare / dof = 960.433 / (963-58), prob = 0.0980324, log(det(Covariance)) = -21069
FMIN Value = 480.216266 at:
beta = 1.400000
(1+beta)*bias = -0.336000
gamma-bias = 3.800000
gamma-beta = 0.000000
Xi y-0-0 = 6.419652 +/- 0.685418 $ 6.4 \pm 0.7 $
Xi y-0-1 = 3.718524 +/- 0.409617 $ 3.7 \pm 0.4 $
Xi y-0-2 = 3.874894 +/- 0.384302 $ 3.9 \pm 0.4 $
...
Both of these fits output their parameters in a format that can be used as input to a multipole fit, and print a message like this:
Use the following config options to refit this data using the fitted multipoles:
data = mock_ell02_multipoles
data-format = comoving-multipole
axis1-bins = {40,45,50,55,60,65,70,75,80,85,90,95,100,105,110,115,120,125,130,135,140,145,150,155,160,165,170,175,180}
axis2-bins = {0,2,4}
axis3-bins = {2.25}
Next, fit using the config options given above (need to comment out load-icov in comoving-xi.ini first, and binning options must be quoted on the command line). Results are essentially identical to those above, as expected, although the fit now has npar = nbins so the chisq is meaningless. First, the ell=0,2,4 multipoles:
./baofit -i ../config/comoving_xi.ini --data mock_ell024_multipoles --data-format comoving-multipole \
--xi-points 40,45,50,55,60,65,70,75,80,85,90,95,100,105,110,115,120,125,130,135,140,145,150,155,160,165,170,175,180 \
--axis1-bins "{40,45,50,55,60,65,70,75,80,85,90,95,100,105,110,115,120,125,130,135,140,145,150,155,160,165,170,175,180}" --axis2-bins "{0,2,4}" --axis3-bins "{2.25}" \
--lmin 0 --lmax 4 --output-prefix mock_refit_ell024_
Fit is ill-conditioned with nbins = 87, npar = 87, chiSquare = 3.20323e-06
Xi y-0-0 = 6.139555 +/- 0.697306 $ 6.1 \pm 0.7 $
Xi y-0-1 = 3.835892 +/- 0.418932 $ 3.8 \pm 0.4 $
Xi y-0-2 = 3.794711 +/- 0.391574 $ 3.8 \pm 0.4 $
...
Second, the ell = 0,2 multipoles (where we need to fix the ell=4 parameters, as above):
./baofit -i ../config/comoving_xi.ini --data mock_ell02_multipoles --data-format comoving-multipole \
--xi-points 40,45,50,55,60,65,70,75,80,85,90,95,100,105,110,115,120,125,130,135,140,145,150,155,160,165,170,175,180 \
--axis1-bins "{40,45,50,55,60,65,70,75,80,85,90,95,100,105,110,115,120,125,130,135,140,145,150,155,160,165,170,175,180}" --axis2-bins "{0,2,4}" --axis3-bins "{2.25}" \
--lmin 0 --lmax 2 --model-config="fix[Xi y-4-*]=0" --output-prefix mock_refit_ell02_
Fit is ill-conditioned with nbins = 58, npar = 58, chiSquare = 1.1299e-06
Xi y-0-0 = 6.419722 +/- 0.685418 $ 6.4 \pm 0.7 $
Xi y-0-1 = 3.718507 +/- 0.409617 $ 3.7 \pm 0.4 $
Xi y-0-2 = 3.874931 +/- 0.384302 $ 3.9 \pm 0.4 $
...
Finally, do the original cosmology fit to the multipoles in several different ways. First, fit ell = 0,2,4 to use the full multipole information:
./baofit -i ../config/comoving.ini --data mock_ell024_multipoles --data-format comoving-multipole \
--axis1-bins "{40,45,50,55,60,65,70,75,80,85,90,95,100,105,110,115,120,125,130,135,140,145,150,155,160,165,170,175,180}" --axis2-bins "{0,2,4}" --axis3-bins "{2.25}" \
--lmin 0 --lmax 4 --dist-add "" --dist-mul "" --output-prefix mock_ell024_fit024_
Fit results: chiSquare / dof = 105.75 / (87-3), prob = 0.0545525, log(det(Covariance)) = -2073.32
FMIN Value = 52.874966 at:
beta = 1.414014 +/- 0.068171 $ 1.41 \pm 0.07 $
BAO alpha-parallel = 1.001841 +/- 0.018064 $ 1.002 \pm 0.018 $
BAO alpha-perp = 0.970763 +/- 0.028428 $ 0.971 \pm 0.028 $
FMIN Errors & Correlations =
beta : 0.068171
BAO alpha-parallel : -0.013024 0.018064
BAO alpha-perp : 0.025535 -0.405439 0.028428
Next, only use the ell = 0,2 subset of the full ell = 0,2,4 dataset (and covariance) in the fit (by changing lmax):
./baofit -i ../config/comoving.ini --data mock_ell024_multipoles --data-format comoving-multipole \
--axis1-bins "{40,45,50,55,60,65,70,75,80,85,90,95,100,105,110,115,120,125,130,135,140,145,150,155,160,165,170,175,180}" --axis2-bins "{0,2,4}" --axis3-bins "{2.25}" \
--lmin 0 --lmax 2 --dist-add "" --dist-mul "" --output-prefix mock_ell024_fit02_
Fit results: chiSquare / dof = 55.859 / (58-3), prob = 0.44235, log(det(Covariance)) = -1409.34
beta = 1.445337 +/- 0.076822 $ 1.45 \pm 0.08 $
BAO alpha-parallel = 1.015529 +/- 0.021743 $ 1.016 \pm 0.022 $
BAO alpha-perp = 0.951949 +/- 0.031385 $ 0.952 \pm 0.031 $
FMIN Errors & Correlations =
beta : 0.076822
BAO alpha-parallel : -0.016388 0.021743
BAO alpha-perp : 0.023216 -0.563814 0.031385
Next, fit the ell = 0,2 dataset:
./baofit -i ../config/comoving.ini --data mock_ell02_multipoles --data-format comoving-multipole \
--axis1-bins "{40,45,50,55,60,65,70,75,80,85,90,95,100,105,110,115,120,125,130,135,140,145,150,155,160,165,170,175,180}" --axis2-bins "{0,2,4}" --axis3-bins "{2.25}" \
--lmin 0 --lmax 2 --dist-add "" --dist-mul "" --output-prefix mock_ell02_fit02_
Fit results: chiSquare / dof = 62.8448 / (58-3), prob = 0.218285, log(det(Covariance)) = -1409.72
beta = 1.427838 +/- 0.075144 $ 1.43 \pm 0.08 $
BAO alpha-parallel = 1.015978 +/- 0.021666 $ 1.016 \pm 0.022 $
BAO alpha-perp = 0.951570 +/- 0.031220 $ 0.952 \pm 0.031 $
FMIN Errors & Correlations =
beta : 0.075144
BAO alpha-parallel : -0.016458 0.021666
BAO alpha-perp : 0.023123 -0.563685 0.031220
| Fit | Dataset Binning | Nbins | Cuts | Nbins(cut) | alpha(par) | alpha(perp) |
|---|---|---|---|---|---|---|
| 1 | 0 <= rP,rT <= 200 | 40^2^ | 40 <= r <= 180 | 963 | 1.002 +- 0.018 | 0.972 +- 0.028 |
| 2 | 40 <= r <= 180, ell = 0,2,4 | 3*29 | none | 87 | 1.002 +- 0.018 | 0.971 +- 0.028 |
| 3 | 40 <= r <= 180, ell = 0,2,4 | 3*29 | ell = 0,2 | 58 | 1.016 +- 0.022 | 0.952 +- 0.031 |
| 4 | 40 <= r <= 180, ell = 0,2 | 2*29 | none | 58 | 1.016 +- 0.022 | 0.952 +- 0.031 |
Add the options --model-config "binning[BAO alpha-p*]={0.9:1.1}*41" --parameter-scan --ndump 0 to generate the chisq scans for fits 1 and 4, marginalized over beta:
./baofit -i ../config/comoving.ini --data mock --load-icov --dist-add "" --dist-mul "" --output-prefix mock_fit_ --model-config "binning[BAO alpha-p*]={0.8:1.2}*81" --parameter-scan --ndump 0
./baofit -i ../config/comoving.ini --data mock_ell02_multipoles --data-format comoving-multipole \
--axis1-bins "{40,45,50,55,60,65,70,75,80,85,90,95,100,105,110,115,120,125,130,135,140,145,150,155,160,165,170,175,180}" --axis2-bins "{0,2,4}" --axis3-bins "{2.25}" \
--lmin 0 --lmax 2 --dist-add "" --dist-mul "" --output-prefix mock_ell02_fit02_ --model-config "binning[BAO alpha-p*]={0.8:1.2}*81" --parameter-scan --ndump 0
Use Mathematica to load chi-square scans:
Needs["DeepZot`BaoFitTools`"]
loadFitAnalysis[fit1scan, "mock_fit_scan", path -> "/Users/david/Cosmo/LyAlpha/code/baofit/build"]
loadFitAnalysis[fit4scan, "mock_ell02_fit02_scan", path -> "/Users/david/Cosmo/LyAlpha/code/baofit/build"]
and make plots at 68% and 95% CL:
Needs["DeepZot`StatisticsTools`"]
With[{
plist = {8, 7}, (* 8 = alpha(perp), 7 = alpha(par) *)
levels = gaussianChiSquareContourLevel[{0.68, 0.95}, 2]
},
Show[{
createFrame[Plot, {0.84, 1.16}, {0.84, 1.16}, AxesOrigin -> {1, 1}, AxesStyle -> Dotted, AspectRatio -> 1,
FrameLabel -> {"\[Alpha](perp)", "\[Alpha](par)"}, LabelStyle -> Large, ImageSize -> 500],
ListContourPlot[fitAnalysisSamples[fit1scan, parameters -> plist],
ContourStyle -> Red, Contours -> levels, ContourShading -> None],
ListContourPlot[fitAnalysisSamples[fit4scan, parameters -> plist],
ContourStyle -> Directive[Dashed, Blue], Contours -> levels, ContourShading -> None]
}]]
{{attachment:chisq.png}}