Reduced chi square of Planck likelihood estimation

[Feng-Quan Wu]

Hi Antony, hi everyone,

We are trying to estimate the reduced chi square for comparing the fitting goodness between different data sets. But we don't understand the chi square we got with cosmoMC.

With Planck data, we got a chi square about 10000, and trying to figure out the number of data points. By reading the Planck's paper, it seems that, for the high-l Planck data, the likelihood function is estimated by using the band power, C_l. If the l range is from 50 to 2500, and consider 4 frequency maps, 100x100, 143x143, 217x217 and 143x217, the data points for Planck high-l is up to about 9800. For this part, is it correct?

For the low-l and polarization part, it seems the likelihood function is not estimated by using the same method as high-l. And we got a negative chi square. So in this case, how can we get the reduced chi square?
Thanks.

[Antony Lewis]

You can't really, only relative chi-squareds. As you say the low L likelihood is not normalized, and at high L the absolute value is not correct anyway because of known bugs in the likelihood (see notes in updated parameter paper). However chi-square differences should still be reliable for most parameters.

[Feng-Quan Wu]

Thank Antony!