🚀 go-pugleaf

juber@uceng.UC.EDU (james uber) writes:

>I obtain parameter estimates via maximum likelihood where
>my model is in the standard reduced form y = f(p), y are the
>data and p are the parameters. I assume that the distribution
>of the model + measurement errors is normal with zero mean
>and known covariance matrix Ve. Thus i am solving the optimization
>problem:

>	min Tr(y - f(p))Inv(Ve)(y - f(p))
>         p

[rest of post deleted]

I do not understand the question.  If y = f(p) (where f is presumably
a known and fixed function of the parameters) and y is observed then
there is no measurement error.  Perhaps you meant y = f(p) + e where e
is a vector of measurement errors.  (This seems implicit in your
description of the nonlinear least squares procedure.)

But you also refer to "model errors".  What are these and how do they
fit in?  If the model is really

              y = f(p) + <error>

and f(p) is known (up to the parameters p) and fixed, then
Var(y) = Var(<error>) regardless of the source of the errors.

Please clarify.