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Asymptotic Optimality Theory for Active Quickest Detection with Unknown PostChange Parameters.

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Summary
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This study introduces a new algorithm for quickly detecting changes in systems with multiple data streams. The proposed method efficiently minimizes detection delays while adhering to sampling constraints.

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Area of Science:

  • Statistics
  • Signal Processing
  • Control Theory

Background:

  • Quickest detection problems aim to minimize delay after a system change.
  • Sampling constraints limit data acquisition from multiple streams.
  • Unknown post-change parameters complicate detection.

Purpose of the Study:

  • To develop an efficient algorithm for quickest detection under sampling control constraints.
  • To address scenarios with unknown post-change parameters in one of p local streams.
  • To minimize detection delay while managing false alarm and sampling limitations.

Main Methods:

  • A greedy-cyclic-sampling-based algorithm is proposed.
  • The algorithm operates under the constraint of observing only one stream per time instant.
  • Asymptotic optimality is analyzed concerning detection delay.

Main Results:

  • The proposed algorithm is shown to be asymptotically optimal.
  • It effectively minimizes detection delay under both false alarm and sampling control constraints.
  • Numerical studies demonstrate the algorithm's effectiveness and applicability.

Conclusions:

  • The greedy-cyclic-sampling algorithm provides an efficient solution for quickest detection problems with sampling constraints.
  • It offers a practical approach for systems with unknown post-change parameters.
  • The method is validated through simulations, confirming its performance.