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Table 2
Review of advantages and disadvantages of measuring spectra vs. fields to infer an ISW detection (top). Review of statistical methods in the literature and their respective advantages and disadvantages (bottom).
Measured | Advantage | Disadvantage | |
quantity | |||
|
|||
Methods exist for calculation with missing data. | Assumes C(ℓ)’s or estimator are Gaussian. | ||
Spectra | Can easily introduce tomography. | Most methods requires | |
to estimate of the covariance matrix. | |||
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Fields | No assumption about galaxy/matter density field | Missing data is an ill-posed problem | |
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Statistical | Advantage | Disadvantage | |
method | |||
|
|||
Simple correlation | Independent of cosmology. | Measure of significance | |
(spectra/fields) | assumes test distribution to be Gaussian | ||
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Amplitude estimation | Detection depends on cosmology/model | ||
(spectra/fields) | Validates signal and model simultaneously | Measure of significance assumes estimator is Gaussian | |
Assumes underlying theory (e.g., ΛCDM) is correct | |||
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χ2 (spectra/fields) | Assumes C(ℓ)’s are Gaussian (spectra) | ||
Validates signal and model simultaneously. | Only gives confidence of rejecting null hypothesis | ||
Assumes underlying theory (e.g., ΛCDM) is correct. | |||
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Model comparison | Asks a different question than other tests. | ISW signal usually too weak to be detected this way | |
(spectra) | Assumes underlying theory (e.g., ΛCDM) is correct |
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