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The iterative proportional fitting procedure (IPF-P) is an algorithm to compute approximately probability measures with prescribed marginals. We propose two extensions of the IPF-P, called conditional iterative proportional fitting procedures (CIPF-P), so that, additionally, given conditional distributions are taken into account. This modification is carried out by using the geometrical interpretation of the IPF-P as successive application of I-projections. Finally, we establish the convergence of both CIPF-Ps in the finite discrete case.

PROBABILITY MEASURES WITH GIVEN MARGINALS AND CONDITIONALS: I-PROJECTIONS AND CONDITIONAL ITERATIVE PROPORTIONAL FITTING