Abstract
An aspect of the measurement selection problem-the existence of anomalous orderings on the probability of error obtained by selected subsets of measurements-is discussed. It is shown that for any ordering on the probability of error as a function of the subset of measurements (subject to an obvious set monotonicity condition), there exists a multivariate normal two-hypothesis problem N(μ,K) versus N(μ,K) that exhibits this ordering. Thus no known nonexhaustive sequential k-measurement selection procedure is optimal, even for jointly normal measurements.
Keywords
Monotonic functionSelection (genetic algorithm)Set (abstract data type)MathematicsProbability of errorMultivariate normal distributionMultivariate statisticsFunction (biology)CombinatoricsStatisticsAlgorithmComputer scienceBiologyMathematical analysisArtificial intelligence
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Publication Info
- Year
- 1977
- Type
- article
- Volume
- 7
- Issue
- 9
- Pages
- 657-661
- Citations
- 256
- Access
- Closed
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Cite This
Thomas M. Cover,
Jan Van Campenhout
(1977).
On the Possible Orderings in the Measurement Selection Problem.
IEEE Transactions on Systems Man and Cybernetics
, 7
(9)
, 657-661.
https://doi.org/10.1109/tsmc.1977.4309803
Identifiers
- DOI
- 10.1109/tsmc.1977.4309803