TO CONDITION, OR NOT TO CONDITION, THAT IS THE QUESTION Between
the completely conditional world of Bayesian inference and the
completely unconditional world of frequentist inference lies the
hazy world of conditional inference. The extremes are easy. In
Bayesian-land you condition on all of the data. In Frequentist-
land, you condition on nothing. If your feet are firmly planted
in either of these idyllic places, read no further! Because,
conditional inference is: The undiscovered Country, from whose
bourn No Traveller returns, Puzzles the will, And makes us
rather bear those ills we have, Than fly to others that we know
not of. 1. The Extremes As I said above, the extremes are easy.
Let’s start with a concrete example. Let be a sample from .
Suppose we want to estimate ; for example, could be the mean of
. Bayesian Approach: Put a prior on . After observing the data
compute the posterior for . This induces a posterior for given .
We can then make statements like The statements are conditional
on . There is n