Ryan Boyden edited subsection_Intensity_statistics_We_show__.tex  almost 8 years ago

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The Cramer statistic is by definition 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\% of the integrated-intensity values. The statistic exhibits a behavior different from that of the other intensity statistics. As figure ??? shows, the Cramer statistic displays very large distances between purely turbulent runs and runs with any degree of feedback. Wind strength appears less important to the statistic than wind presence does, which indicates a binary sensitivity to stellar-mass loss rates. The Cramer statistic is also sensitive to magnetic field strength, as seen in the varying distances between the purely turbulent models.  Considering the various degrees of sensitivity, we find the PCA to be strong a candidate for constraining feedback signatures. As Figure 3 shows, this statistic displays sharp, distinct features for a strong wind model, and its color-plot only shows strong sensitivity to changes in stellar-mass loss rate. The other intensity statistics either exhibit less-distinct features, or react to multiple physical changes. Because of this, we recommend using these statistics in concert with the PCA. Of the remaining intensity statistics, the SCF is the second most promising candidate, as its color-plot behaves similarly similar  to the PCA.