[0809.4624] CMB likelihood approximation by a Gaussianized
Posted: September 29 2008
This paper investigates approximations for the CMB temperature likelihood function at low l, in particular an approximation that can be calibrated from Gibbs sampling. They claim a surprisingly large shift in some cosmological parameters (n_s by 0.6 sigma) when using the new approximation compared to WMAP. If correct this is quite interesting and surprising.
Some comments:
* Compressing the data into power spectrum estimators, as WMAP do at high l, should be suboptimal but unbiased as long as a valid likelihood approximation is used. I'm therefore surprised to see apparent shifts in parameters rather than changes in the error bar. When testing with simulations, I've found that the WMAP-like likelihood approximations work just fine. Even evident deviations from the assumed likelihood model has almost no effect because the errors tend to cancel between l (see 0804.3865). Indeed just using a pure-Gaussian likelihood approximation works fine in almost all realisations. I'm sure WMAP have also extensively tested their method for biases in simulations. I wonder if the authors reproduce such shifts in idealized simulations?
* This being the case, could the shifts be due to something else, e.g. differences in beam modelling? The paper doesn't comment on what they do about the beams at low l, even though the beam transfer function is not unity even at l<200.
* In the conclusions they comment that their approach allows seamless propagation of systematic effects such as beam errors. I'm not convinced by this: a beam error essentially shifts the entire spectrum up and down. The approximation used in the paper fits the maginalized C_l distributions at each l separately, which in the case of beam errors are actually strongly correlated between l. Is there any reason to expect this to work?
Some comments:
* Compressing the data into power spectrum estimators, as WMAP do at high l, should be suboptimal but unbiased as long as a valid likelihood approximation is used. I'm therefore surprised to see apparent shifts in parameters rather than changes in the error bar. When testing with simulations, I've found that the WMAP-like likelihood approximations work just fine. Even evident deviations from the assumed likelihood model has almost no effect because the errors tend to cancel between l (see 0804.3865). Indeed just using a pure-Gaussian likelihood approximation works fine in almost all realisations. I'm sure WMAP have also extensively tested their method for biases in simulations. I wonder if the authors reproduce such shifts in idealized simulations?
* This being the case, could the shifts be due to something else, e.g. differences in beam modelling? The paper doesn't comment on what they do about the beams at low l, even though the beam transfer function is not unity even at l<200.
* In the conclusions they comment that their approach allows seamless propagation of systematic effects such as beam errors. I'm not convinced by this: a beam error essentially shifts the entire spectrum up and down. The approximation used in the paper fits the maginalized C_l distributions at each l separately, which in the case of beam errors are actually strongly correlated between l. Is there any reason to expect this to work?