L-infinity metric criteria for convergence in Bayesian recursive inferencesystems

Motivated by applications to probabilistic inference, we consider a sequenc e of probability measures, called "conclusion measures," on a fixed space X . The sequence is generated recursively via conditional probability, driven by a sequence of input measures (rather than by a sequence of punctual dat a, as in Bayesian statistical inference). The general problem is to give co nditions on the input measures such that the sequence of conclusion measure s converges weakly. We develop L-infinity-metric criteria defined recursive ly on the input measures, which are sufficient (but not necessary) for the sequence of conclusion measures to converge at a given rate. We discuss the applications of this to the "directed convergence strategy" introduced in [1]. Finally, we show that if the input measures satisfy the criteria, then the input sequence also converges at a comparable rate. (C) 1999 Academic Press.