Random variables have a **prior distribution** and a
**posterior distribution**.
Denote the prior by *b*_{i} (for ``before")
and posterior by *a*_{i} (for ``after").
Define *p*_{i}=*a*_{i}/*b*_{i},
and insert *p*_{i} in any of the inequalities above.
Now suppose we have an adjustable model parameter
upon which the *a*_{i} all depend.
Suppose we adjust that model parameter to try to make
some Jensen inequality into an equality.
Thus we will be adjusting it
to get all the *p*_{i} equal to each other, that is,
to make all the posteriors
equal to their priors.
It is nice to have so many ways to do this,
one for each Jensen inequality.
The next question is,
which Jensen inequality should we use?
I cannot answer this directly,
but we can learn more about the various inequalities.

10/21/1998