[ADMB Users] citation for empirical Bayes variance computation
otter at otter-rsch.com
Fri May 7 08:05:47 PDT 2010
It came out of my head.
Reasoning is as follows. Let the RE's be u and the other parameters
Let uhat(x) be the value of u which maximizes the function
(joint probability dist if you are a Bayesian) l(x,u)
of x and u for a given value of x. Then the delta method gives the
estimate for the variance of uhat as
trans(uhat'(x)) * inv(log(L)_xx)* uhat'(x)
where L(x) = int l(x,u) du
If uhat(x) is known then a candidate for the variance of u would be
so add them together to reflect the fact that uncertainly in the
x gives uncertainty in the value of uhat.
So it just seems like a reasonable calculation. Of course in nonlinear
models this approximation can be quite bad in more extreme cases.
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