So we were installing what's called an " eddy covariance tower, " which is a series of instruments that measures the exchange of greenhouse gases, like carbon dioxide and methane, between the land and the atmosphere.

所以我们安装了一个被称为“涡度协方差塔”的装置，这种装置由多种仪器构成，用于测量地面与大气温室气体的交换，例如二氧碳和甲烷。

So this is, I mentioned that before, variance-invariance, covariance regularization.

所以这就是我之前提到的，方差变性协方差正则。

Instead of looking for direct physical contact, it looks for statistical co-occurrence, basically covariance.

寻找直接的物理接触，而是寻找统计上的，本质上是协方差。

Now, this right here-- so everything we've learned right now-- this right here is the covariance, or this is an estimate of the covariance of X and Y. Now what is this over here?

，这里的内容——我们刚刚学到的——这就是协方差，或者说是X和Y协方差的一个估计值。 那么这里的这个是什么呢？

And then we do the covariance between the vertical movements of wind and the concentration of gas.

然后我们计算风的垂直运动和气体浓度之间的协方差。

Well, you could view this as the covariance of X with X. But we've actually already seen this.

好吧，你可以将这视为X与自身的协方差。 但实际上我们已经见过这个概念了。

That means variance, invariance, covariance, regularization.

那意味着方差、变性、协方差、正则。

It's called an eddy covariance tower.

被称为涡流协方差塔。

The covariance of a random variable with itself is really just the variance of that random variable.

一个随机变量与自身的协方差其实就是该随机变量的方差。

Gosselin: So on the tower for eddy covariance, in principle, there's two main instruments: one instrument that measures the concentration of gas that we're interested in in the air and [another] that uses infrared.

Gosselin：原则上，涡流协方差塔上有两种主要仪器：一种测量空气中我们感兴趣的气体浓度，[另一种]使用红外线。

If they both go up together, they would have a positive variance or they both go down together.

如果们一起增加，们就会有正的协方差，或者们一起减少。

And if we kept doing this, let's say for the entire population this happened, then it would make sense that they have a negative covariance.

如果我们继续这样做，假设这种情况发生整个总体中， 那么们具有负协方差就说得通了。

And the degree to which they do it together will tell you the magnitude of the covariance.

们一起变的程度将告诉你协方差的大小。

Now we don't know the entire covariance, we only have one sample here of this random variable.

我们知道整个协方差，我们这里只有一个随机变量的样本。

I want to connect to this definition of covariance to everything we've been doing with least squared regression.

我想将协方差的这个定义与我们一直做的最小二乘回归的内容联系起来。

Hopefully that gives you a little bit of intuition about what the covariance is trying to tell us.

希望这能给你一点关于协方差想要告诉我们的直觉。

And really it's just kind of a fun math thing to do to show you all of these connections, and where, really, the definition of covariance really becomes useful.

这其实只是一个有趣的数学小知识，展示所有这些联系，并说明协方差的定义何处真正变得有用。