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**A Markovian procedure for assessing the state of a system.**
*(English)*
Zbl 0654.92020

Authors’ summary: We consider a class of systems, the states of which can be represented by particular subsets of features in a basic set. A procedure for assessing the state of a system in which the presence of a particular feature is tested on each trial is described. The feature is chosen so that the outcome of the test is as informative as possible. This outcome results in a modification of a class of plausible states. The sequence of plausibilities is a finite Markov chain.

Results of practical significance are obtained and cover cases in which the response data are noisy, and the state of the system may even change randomly from trial to trial. An application of primary interest to the authors is the assessment of knowledge. In this case, the systems are human subjects, the features are questions or problems, and the state of an individual is that particular subset of questions that the individual is capable of solving. The conditions investigated in the paper, even though primarily dictated by this application, are nevertheless of general scope.

Results of practical significance are obtained and cover cases in which the response data are noisy, and the state of the system may even change randomly from trial to trial. An application of primary interest to the authors is the assessment of knowledge. In this case, the systems are human subjects, the features are questions or problems, and the state of an individual is that particular subset of questions that the individual is capable of solving. The conditions investigated in the paper, even though primarily dictated by this application, are nevertheless of general scope.

Reviewer: I.Křivý

### MSC:

91E99 | Mathematical psychology |

60J20 | Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) |

60J10 | Markov chains (discrete-time Markov processes on discrete state spaces) |

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\textit{J. Cl. Falmagne} and \textit{J. P. Doignon}, J. Math. Psychol. 32, No. 3, 232--258 (1988; Zbl 0654.92020)

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### References:

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