L∞ Metric Criteria for Convergence in Bayesian Recursive Inference Systems
✍ Scribed by Bruce M. Bennett; Rachel B. Cohen
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 126 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0196-8858
No coin nor oath required. For personal study only.
✦ Synopsis
Motivated by applications to probabilistic inference, we consider a sequence of probability measures, called ''conclusion measures,'' on a fixed space X. The sequence is generated recursively via conditional probability, driven by a sequence Ž of input measures rather than by a sequence of punctual data, as in Bayesian . statistical inference . The general problem is to give conditions on the input measures such that the sequence of conclusion measures converges weakly. We develop L ϱ -metric criteria defined recursively on the input measures, which are Ž . 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 w x 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.