CosmoMC: Chi-sq with action=2 vs action=4

[Jose Lozano]

Hello,

I'm running a dark energy model with a dynamical equation of state (already tested). However, by INCLUDING Planck 2018 likelihoods I find different values of chi-square with action =4 vs action = 2. When I run action=4 in CosmoMC, the values of the chi-square are the following:

loglike chi-sq
995.932 1991.864 CMB: plik = plik_rd12_HM_v22_TT
18.357 36.714 CMB: lowl = commander_dx12_v3_2_29
255.991 511.981 SN: JLA PantheonPlus
0.004 0.008 BAO: DR1BGSbao
4.461 8.922 BAO: DR1LRGbao
1.169 2.337 BAO: DR1LRG_ELGbao
0.135 0.271 BAO: DR1ELGbao
0.079 0.157 BAO: DR1QSRbao
0.497 0.994 BAO: DR1LYAbao

On the other hand, finding the best-fit values with action=2 in CosmoMC, the values of the chi-square are:

483.434 966.869 CMB: plik = plik_rd12_HM_v22_TT
21.284 42.567 CMB: lowl = commander_dx12_v3_2_29
255.772 511.544 SN: JLA PantheonPlus
1.621 3.241 BAO: DR1BGSbao
15.384 30.767 BAO: DR1LRGbao
1.719 3.439 BAO: DR1LRG_ELGbao
1.644 3.288 BAO: DR1ELGbao
0.094 0.189 BAO: DR1QSRbao
1.103 2.206 BAO: DR1LYAbao

In our .ini file, the parameters vary with reasonable bounds:

param[tau] = 0.058 0.01 0.8 0.01 0.005
param[omegabh2] = 0.0225 0.005 0.1 0.0001 0.0001
param[omegach2] =0.116 0.001 0.99 0.001 0.0005
param[theta]= 1.0411 0.5 2 0.0004 0.0004
param[calPlanck]= 0.9999 0.9 1.1 0.002 0.0005
param[acib217] = 64 0 200 10 1.2
param[xi] = 0.2576 0 1 0.1 0.1
param[asz143]= 0.6973563E+01 0 10 2 0.6
param[aps100] = 0.2506704E+03 0 400 24 17
param[aps143] = 0.4360550E+02 0 400 10 3
param[aps143217] = 0.4136439E+02 0 400 12 2
param[aps217] = 0.1022745E+03 0 400 13 2.5
param[aksz] = 0.2921053E-03 0 10 3 1
param[kgal100] = 8.99 0 50 2 1
param[kgal143] = 10.71 0 50 2 1
param[kgal143217] = 17.80 0 100 4 1.5
param[kgal217] = 82.25 0 400 15 2
param[cal0] = 0.997 0 3 0.001 0.0005
param[cal2] = 0.995 0 3 0.002 0.001


As you can see, the chi-square of BAO and CMB shows a discrepancy running action=4 in comparison with running=2.
I hope you can give me some hint or a possible solution to solve this issue. This occurs when Planck 2018 likelihoods are taken into account.

I'm looking forward to your kind help,

Best regards,
Jose Lozano

[Antony Lewis]

Is action=4 run with central parameters equal to the best-fit found (for all parameters)?

[Jose Lozano]

Hello Anthony,

Thanks for the reply. No, the central values for all parameters ARE NOT to those found in the best fit when running action = 4 but are approximated to those best fit values.
I have been running action = 2 many times (with central values given previously in this post) and finding the chi-sq totally different. This happens when CMB dataset is included. Without CMB, the chi-sq values after running action = 2 and action = 4 are in agreement.

[Antony Lewis]

You don't quote the amplitude parameter, my guess is it's slightly different (and possibly tau or nuisance parasmeters), e.g. some seem to have only 2 sf but best-fit should have more sf.

[Jose Lozano]

Yes, you're right. we don't include param[logA] and we use some best-fit values in our ini file so some have 2 sf. Hence, your recommendation is to use the best fit values found after running action=2 in our ini file as our central values, and rerun action = 2 once again? I don't understant why chi-square in BAO changes when CMB likelihood is included.

I should expect that the chi-sq values after running action=4 must be the same when running action=2.