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Again, normalization can also be ensured by parameterization of
and solving for unnormalized probabilities , i.e.,
|
(174) |
The corresponding functional reads
|
(175) |
We have
|
(176) |
with diagonal matrix
built analogous to and ,
and
|
(177) |
|
(178) |
The diagonal matrices
commute,
as well as
,
but
.
Setting the gradient to zero and using
|
(179) |
we find
|
(180) |
with -gradient
=
of
and the corresponding diagonal matrix.
Multiplied by this gives the stationarity equation (172).
Next: The Hessians ,
Up: Gaussian prior factor for
Previous: Lagrange multipliers: Error functional
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Joerg_Lemm
2001-01-21