Eddy?

They're going to Eddy in Lagos.

Is the covariance large, medium, or small?

All we represented was a vector, the mean, and the covariance matrix, and the covariance matrix is quadratic.

Now I'm going to ask you about the covariance.

From there, I can get the variance covariance matrix.

It does help reinforce the concept, of correlation and covariance.

And covariance was just sum of cross products divided by n.

Say we have a prior of a Gaussian with a mean mu and covariance sigma squared, and our measurement has exactly the same mean and same covariance.

The measurement has a mean of nu and a covariance of r squared.

Remember from the lecture on correlation, then, that represents the covariance or correlation.

That is, the covariance is smaller than either of the two covariances in isolation.

Yes, there is. It turns out the omega matrix is the inverse covariance matrix.

I didn't really talk much about this, but it is really the inverse covariance matrix.

We calculated some basic statistics, such as the mean, the standard deviation, and the covariance.

This over here is kind of a mixed variance. This is often called the covariance.

But the way Mrs. Eddy structured the Committee office, there are a lot of resources available, too, around the world.

Contributes to the correlation, to covariance, and we'll contribute to the slope of the regression line.

The covariance matrix would look exactly as before, because it's not affected by the measurements themselves.

Now, b is also easily expressed using the covariance, but now we're normalizing by the variance of x.

And if we pre and post multiply that by the variance covariance matrix, that gives us, the correlation matrix.

If you just invert that matrix, you get the full covariance for all of the landmarks and the robot.

Going into the covariance, we see values along the main diagonals 0.05, 0.05, 0.33, and 0.33 for the velocities.

It has a mean over here called mu, and this example has a much smaller covariance for the measurement.

I also have a covariance that characters my uncertainty, and that is updated as follows, where T is the transpose.

This is called often covariance if you've normalized, because it is the variance calculation of a two co occuring variables.

There's a new covariance matrix, and for the third observation followed by the prediction, the prediction is correctly effectively 4, 3.999.

I thought of a dry leaf imprisoned in an eddy of wind, while a mysterious apprehension, a load of indefinite doubt, weighed me down in my chair.

I also want you to output the covariance matrix, which has certain elements that are still 0, like these guys over here.

The formulas for calculating Mu and the covariance matrix Sigma generalize the ones we studied before and they are given over here.

So there we went from the raw data to, the variance, covariance matrix and the correlation matrix all using this new skill, metrical algebra.

When you estimate covariance from data and try to understand which direction they point, this kind of eigenvalue anylysis gives you the right answer.

EM is a probabilistic generalization that also allows you to find clusters but also modifies the shapes of the clusters by modifying the covariance matrix.

Suppose we have a prior that sits over here and a measurement probability that sits over here really far away and both have the same covariance.

All we have to do, is take a diagonal matrix that has the standard deviations, so that's just the square root, of, the, diagonal entries of the variance covariance matrix.

The mountain bike came from users, came from young users, particularly a group in Northern California, who were frustrated with traditional racing bikes, which were those sort of bikes that Eddy Merckx rode, or your big brother, and they're very glamorous.

The basic idea is that for any Gaussian no matter what the mean and the covariance is, you can state how far inner out a point axis, so let me give you an example.

Once I've done this, I know µ, and then I can finally plug it in here, but now I have to go through the data again and compute this guy, so we can finally get to my covariance.

P is the initial uncertainty, and I want you to initialize it so that the uncertainty for the x,y coordinates is zero, but the covariance term for the velocities is 1000, indicating that we really don't know the initial velocity.

Now, Van Gogh doesn't know anything about physics, but I think it's very interesting that there was some work done to show that this eddy pattern in this painting followed a statistical model of turbulence, which brings up the whole interesting idea of maybe some of this mathematical patterns is in our own head.