This paper looks at how well Planck can do at distinguishing n_s \ne 1 models from n_s=1.
Why are the authors using the Gaussian likelihood in Eq. 1 rather than the true likelihood function? It is well known that the Gaussian approximation is not very good, and the true function is just as easy to compute with an effective full sky. (it's given explicitly in e.g. Eq 5 of astroph/0502469, though I certainly wasn't the first to write it down). Do you get out the correct posterior constraints using this function?
[astroph/0605004] Model selection forecasts for the spectral index from the Planck satellite
Authors:  Cédric Pahud, Andrew R Liddle, Pia Mukherjee, David Parkinson 
Abstract:  The recent WMAP3 results have placed measurements of the spectral index n_S in an interesting position. While parameter estimation techniques indicate that the HarrisonZel'dovich spectrum n_S=1 is strongly excluded (in the absence of tensor perturbations), Bayesian model selection techniques reveal that the case against n_S=1 is not yet conclusive. In this paper, we forecast the ability of the Planck satellite mission to use Bayesian model selection to convincingly exclude (or favour) the HarrisonZel'dovich model. 
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 Joined: May 02 2006
 Affiliation: University of Sussex
[astroph/0605004] Model selection forecasts for the spectra
Hi Antony,
We used Gaussian likelihoods, for no reason other than that we thought that the nonGaussianity of the likelihood functions for C_2  C_10 will not make a significant difference. But you're right, it is as easy to use the true likelihood function. We'll rerun the analysis through and get back. Our guess is that the result wont change much (as the posteriors look alright), but we'll see.
We used Gaussian likelihoods, for no reason other than that we thought that the nonGaussianity of the likelihood functions for C_2  C_10 will not make a significant difference. But you're right, it is as easy to use the true likelihood function. We'll rerun the analysis through and get back. Our guess is that the result wont change much (as the posteriors look alright), but we'll see.

 Posts: 3
 Joined: May 02 2006
 Affiliation: University of Sussex
[astroph/0605004] Model selection forecasts for the spectra
We have recomputed everything using the improved likelihood function. The updated paper is on astroph today. The numbers changed a little, the paper/results are qualitatively unchanged.