One problem with the estimates for |FA| which come directly from the
Karle/ Hendrickson equations is that the values are not always
reasonable; e.g. sometimes the estimate for |FA| is greater than the
total scattering power of the atoms involved.
Terwilliger (1994)
suggests correcting this by using a Bayesian estimate for |FA|
predicated on the prior expected distribution of values:
P(FA)
exp(-FA
/
),
where
is the expected mean square value of FA within a given
resolution shell, given whatever we know about B values, scattering factors,
etc.
Furthermore we can also use prior knowledge about the likely errors in our
data to condition the probability of the observed quantities
=
1/2(|F+| + |F-|) and
F =
(|F+| - |F-|).
where
After a bit more of this sort of analysis we arrive at the Bayesian
estimate for any quantity <x> that depends on FA,
FT, and
:
The integration should properly run over all three variables
FA, FT,
,
but Terwilliger suggests taking FT as being purely defined by its
most probable value in order to save computational time.