# Update on Fisher forecasts

From CMB-S4 wiki

In this post I briefly summarize the changes that Ben and I implemented on the Fisher forecasts relative to previous iterations. These will all be expanded upon.

- For both map-based forecasts and Fisher forecasts, the previous definition was that noise levels (in power) in the circular 3% mask are 3 times the noise levels in BK. This was an approximation. Noise levels are now appropriately rescaled from BK using the ratios of fsky*w1^2/w2 for the circular mask and BK. This leads to a rescaling by 2.72 instead of 3, resulting in 10% lower noise levels overall.
- Both map-based forecasts and Fisher forecasts previously assumed inverse variance weighting. For most configurations and values of r this is not a good approximation as can clearly be seen in this posting. The new forecasts optimize the weighting used in the analysis, i.e. keeping the noise variance map fixed.
- For both map-based forecasts and Fisher forecasts, NETs were previously taken to be the same for both sites, with the values taken to be the averages of the NETs for the sites taken from this spreadsheet. The new version of forecasts accounts for differences between NETs for the two sites and uses the same values as in the posting. Because currently only 95 GHz maps are available for the different surveys, the elevation dependence is not correctly captured, and it is assumed to be the same as at 95 GHz at all frequencies.
- The noise variance maps provided for the deep Chile survey, the wider pole survey, and the deep pole survey are used to compute relative efforts for the different surveys. The maps are generated assuming the same NETs at 95 GHz as in the posting above. Scaling to the same NET to match Clem's posting, the efficiencies relative to the deep pole survey (v1) are 0.796 for the deep Chile survey (v1), and 0.945 for the wide pole survey (v1), or an efficiency of the deep Chile survey to the wide pole survey of 0.843, consistent with Clem's ratio of 69/82 up to rounding errors.
- Previous map-based simulations and Fisher forecasts assumed that the 20 GHz is rescaled between surveys just like the other SAT frequencies. Since the 20 GHz detectors are on the delensing telescope, there will be no coverage at 20 GHz in the shallow Chile patch. We have updated the forecasts accordingly and include 20 GHz data only in the region that is delensed.

The main difference between the numbers I show by default and the numbers Ben shows by default is filtering, or the fraction of modes observed. By comparing noise covariance matrix with theoretical expectation, one can extract the fraction of modes observed. For r=0, I have confirmed that I agree with Ben's numbers if I incorporate this into my forecasts. This number is likely different between the two sites and this should be studied in more detail.