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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 | |||
|
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| 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 | |||
|
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| 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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