Re: simple way to update the inverse of the covariance matrix with each data point


Ken Butler wrote:
On 25 Sep 2006 17:54:21 -0700, "prieditis@xxxxxxxxxxxxxxxxxxxxxx"
<prieditis@xxxxxxxxxxxxxxxxxxxxxx> wrote:

Is there any simple way to update the inverse of the covariance matrix
as each data point is added or deleted?


The magic words are "Sherman-Morrison-Woodbury formula". This formula
is in Thisted's book "Elements of Statistical Computing", page 117 in
my edition.

Ken, I don't think those are the right magic words because the OP
was asking for the formula for updating the inverse as each DATA
POINT is added (or deleted).

Max's formula is inv (A + UCV) = inv A - (inv A)( ( ....)

and when c is the scaler 1, Max's formula becomes the Sherman-
Morrison formula for

inv (A + uv ) where uv is the product of a column and row
vectors.

You won't need Thisted's book. These formulas are all over the
Google web pages. :-) Rather nifty when they apply.

-- Reef Fish Bob.

.