On adaption with noisy information

J. B. Kadane, G. W. Wasilkowski, H. Woźniakowski

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


When observations can be made without noise, it is known that adaptive information is no more powerful than nonadaptive information for approximation of linear problems with Gaussian measure. When the noise is additive, independent of the true value, and normal, once again adaption does not help (Theorem 1 in Section 4). However, when those conditions are not satisfied, Examples 1 and 2 of Section 4 show that adaptive information can be much more powerful than nonadaptive information. Finally if orthogonal observations are used with the sample size as well as the number of repetitions fixed, and only the directions of observations are chosen adaptively, then once again adaption does not help (Theorem 2 in Section 5). The issue is analogous to whether sequential designs are more powerful than fixed sample size designs in Bayesian statistics.

Original languageEnglish
Pages (from-to)257-276
Number of pages20
JournalJournal of Complexity
Issue number4
StatePublished - Dec 1988

Bibliographical note

Funding Information:
*Research supported by the Office of Naval Research under Contract NOO014-85-K-0539 and the National Science Foundation under Grant BNS 84-11738. tResearch supported by the National Science Foundation under Grant DCR-86-03674. *Research supported by the National Science Foundation under Grant ICT-85-17289.

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Statistics and Probability
  • Numerical Analysis
  • General Mathematics
  • Control and Optimization
  • Applied Mathematics


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