  Probabilities for observations in cosmology are conditioned both on the
universe's quantum state and on local data specifying the observational
situation. We show the quantum state defines a measure for prediction through
such conditional probabilities that is well behaved for spatially large or
infinite universes when the probabilities that our data is replicated are taken
into account. In histories where our data are rare volume weighting connects
top-down probabilities conditioned on both the data and the quantum state to
the bottom-up probabilities conditioned on the quantum state alone. We apply
these principles to a calculation of the number of inflationary e-folds in a
homogeneous, isotropic minisuperspace model with a single scalar field moving
in a quadratic potential. We find that volume weighting is justified and the
top-down probabilities favor a large number of e-folds.
