  We elucidate generally the interference of independent Bose fields in view of
the conditional probability for the particle number measurements, and clarify
its relation to the source number statistics. Despite lack of intrinsic phases,
the interference phase can be inferred from the particle number registered at
one detector by using the classical mean fields. If the conditional number
distributions for the other detectors, given the outcome of the first detector,
exhibit sufficiently narrow peaks around the values specified by the estimated
phases, the mean field description is valid in a single run of interference.
The widths in the conditional distribution are determined by the number
statistics of the sources, among which notable scaling behavior is found
depending on the detector configurations with the boundary at the Poissonian.
The mean field description is found to be applicable to Poissonian and
sub-Poissonian sources, whereas for super-Poissonian sources it is likely
invalidated with the rather broad conditional distribution.
