Table 2
Overview of the sets of summary statistics used.
| ϕ | Dim. | Non-Gaussian | Scale description | Scale coupling |
|---|---|---|---|---|
| mean | 1 | ✗ | ✗ | ✗ |
| var | 1 | ✗ | ✗ | ✗ |
| mean of log | 1 | log-Gauss. | ✗ | ✗ |
| var of log | 1 | log-Gauss. | ✗ | ✗ |
| QF | 10 | ✓ | ✗ | ✗ |
| PS | 6 | ✗ | ✓ | ✗ |
| PS of log | 6 | log-Gauss. | ✓ | ✗ |
![$\[S_1^{I s o}\]$](/articles/aa/full_html/2025/04/aa51493-24/aa51493-24-eq44.png) |
4 | ✓ | ✓ | ✗ |
![$\[\langle S_{2}^{I s o 1}\rangle_{j_{2}-j_{1}}\]$](/articles/aa/full_html/2025/04/aa51493-24/aa51493-24-eq45.png) |
3 | ✓ | ✗ | ✓ |
![$\[\langle S_{2}^{I s o 2}\rangle_{j_{2}-j_{1}}\]$](/articles/aa/full_html/2025/04/aa51493-24/aa51493-24-eq46.png) |
3 | ✓ | ✗ | ✓ |
Notes. We report their dimension, whether they are sensitive to non-Gaussianity, provide a multiscale description, and probe couplings between scales. Here, “log-Gauss.” reminds us that, even if the statistics at stake are not Gaussian, they remain a very partial diagnostic of non-Gaussianity as these are Gaussian with respect to the logarithm of the field.
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