The Prior Info Part of Bayesian Analysis

Hi,

My question deals with whether it is OK to use part of a data set to
make a prior estimate of a parameter's distribution which one is
trying to estimate.

As an example, suppose you are trying to estimate the phase of a
single stationary sinusoid in WGN. It is known that for this case, no
unbiased estimator exists, so it makes sense to try to find the MMSE.
Initially, you have no info as to where the true parameter value lies
in the range [0,2*pi). If you take small sample from the entire data
set however, you can get a rough estimate as to what the phase is and
also a decent CI in which the true param value must lie. The goal
would be to now use this prior info to estimate an initial guess as to
the phase's PDF which could be used with the remaining data set to get
an improved estimate.

Is this type of approach OK to use?
Does it lead to any actual significant benefit?
Does anyone know if this type of approach is covered in a text?

TIA,

Matt Brenneman

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