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I the wikipedia page for scatter matrix, it shows the formula as

enter image description here

The centering matrix does imply the divide by n, but the summation eqn above does not indicate the divide by n. Why is that? it would make sense though, that you must divide by n, so the scatter matrix does not keep on increasing with more samples.

The scatter matrix is used in the posterior wishart distribution as

enter image description here

(substitute x for xi). This means the more you sample, the wider the posterior distribution?

bhomass
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    Dividing a scatter matrix by n or n-1 turns it into covariance matrix, http://stats.stackexchange.com/a/22520/3277. In case of n it will be "biased" or maximum lokelihood covariance. In many instances (of usage within some analysis algorithm) we do not need covariances, scatters will suffice. Likewise we not always need variance - sum-of-squares might do. – ttnphns Dec 11 '16 at 07:48
  • So that leads into my other question. If the scatter matrix is used without dividing by n-1, it will get larger as the number of samples increase. Intuitively its hard to see how that can that be used to determine the posterior wishart distribution. I added an image of the formula in the original question. – bhomass Dec 12 '16 at 19:34
  • Exactly *how* is the scatter matrix "used" in the posterior Wishart distribution? – whuber Dec 12 '16 at 19:49
  • see the last eqn I posted. delta_0 is the prior variance. You add the sum of eta * eta_transpose over samples i, which I believe is the definition of scatter matrix (ignore the sum over z part). The result is the posterior variance. Invert to get back the precision. If you don't divide by n, then the scatter matrix term keeps increasing as you get more samples. – bhomass Dec 13 '16 at 20:49

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