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\subsection{Intensity Statistics}
We show the colorplots for all intensity statistics in Figure ???. With the exception of the Cramer statistic, we find that these statistics exhibit the strongest sensitivities to changes in stellar mass-loss rates. As seen in their colorplots, the largest distances
(given %(given by the darkest
colors) colors--include?)
appear when any strong wind model (W1) is compared to either a weak wind model (W2) or a purely turbulent model (T).The Kurtosis and Skewness are our clearest examples of this, as they capture a sensitivity hierarchy among pairings. These statistics explicitly yield the largest distances between pairs of W1 and T, followed by pairs of W1 and W2.
(should %(should I include: This sort of ordering confirms the notion that a cloud with strong winds is most different from a purely turbulent cloud, followed by a weaker winded one.--Not the best wording but I'm wondering if this sort of blunt statement is necessary, especially since it also slightly addresses time
sensitivities.)And, sensitivities.)
And, they capture similar, weaker sensitivities between pairs of W2 and T.
The sensitivity hierarchy with strong wind models is not as clear in the PDF, SCF, and PCA. For the PDF, this blurring is not only noticeable in comparisons
between involving W1, but also structured in
comparisons those between weaker wind models. We find the blurring to be associated with time
evolution (and evolution, %(and potentially magnetic field strength),
and the structure to be correlated
to with changes in magnetic field strengths. The structure among weak wind models does not occur in the PCA and SCF, since their distances not involving W1 are quite small. Thus, they are weakly sensitive towards magnetic field strength. Here, we only note blurring in our strong wind models.
The Cramer Statistic is defined as a distance metric, so it we include its discussion and analysis here. As described in Yeremi et. al (2014), this statistic compares the interpoint differences between two data sets with the point differences between each individual data set. Following K16, we compute the Cramer Statistic using only the top 20(percent) of our data
set's (integrated) intensity sets' integrated-intensity values. The statistic exhibits a behavior different from that of the other intensity statistics. As seen in its colorplot, we only find very large distances between purely turbulent runs and runs with any degree of feedback. This indicates a sensitivity towards magnetic field
strength (?). strength. %I saw that this was in the conclusion, but I'm not sure how to interpret it. Is this becuase the distances between them and wind models vary with respect to "t"? Is also it not sensitive at all to winds?
Considering these various degrees of sensitivities, we find the PCA to be strong a candidate for constraining feedback signatures. As seen in
figure (PCA-cov_matrix), Figure 3, this statistic outputs sharp, distinct features for a strong wind model, and its color-plot only notes strong sensitivities
for to changes in stellar-mass loss rates. The other intensity statistics either output less-distinct features, or show other sensitivities that may influence
their outputs. (may them.
%(may have to address the PCA pairs of W1T1 and W2T2's).
Because of this, we recommend using these statistics to support what is found with the PCA. Out of all of these secondary statistics, the SCF appears to be the strongest candidate, as its color-plot behaves quite similar to the PCA.
%Although many of the intensity statistics produce color-plots showing a sensitivity to feedback, a few of them yield significant differences in their graphical outputs. After applying our strong wind model (W1) to a purely turbulent one (T2t0), the behaviors in the Skewness, Kurtosis, and SCF do change, but their shapes, end behaviors, and/or slopes remain quite similar.