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

Role of particle-number statistics in interference of independent Bose fields