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How can you have negative covariance? Is this how one cancels systematic uncertainties?

A negative covariance, or ``anti-correlation'', between two variables, just means that when one variable's value goes up, the other's tends to go down (the example I gave in class a few weeks ago was the anti-correlation between weight and jockey speed: the more you weigh, the slower your horse will tend to run). You can see how this works from the definition of covariance: $\sigma_{uv}^2 = \langle (u-\bar{u})(v-\bar{v})\rangle$. If whenever $u$ is larger than $\bar{u}$, $v$ tends to be smaller than $\bar{v}$, and vice versa, the average of the product of deviations will be negative.

Actually covariances are connected to cancellation of systematics, but not necessarily by anti-correlation: positive correlation can help too. For example, if you are trying to measure a small signal on a large background with systematic uncertainties, taking a ratio with another measurement that has correlated systematics will introduce a covariance term that helps reduce the effect of those systematics.


next up previous
Next: Is there possible asymmetry Up: Content Questions Previous: What's the difference between
Kate Scholberg 2014-11-10