On the Sequential Probability Ratio Test in Hidden Markov Models

Authors Oscar Darwin , Stefan Kiefer

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Oscar Darwin
  • Department of Computer Science, Oxford University, UK
Stefan Kiefer
  • Department of Computer Science, Oxford University, UK


The authors thank anonymous referees for valuable suggestions.

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Oscar Darwin and Stefan Kiefer. On the Sequential Probability Ratio Test in Hidden Markov Models. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


We consider the Sequential Probability Ratio Test applied to Hidden Markov Models. Given two Hidden Markov Models and a sequence of observations generated by one of them, the Sequential Probability Ratio Test attempts to decide which model produced the sequence. We show relationships between the execution time of such an algorithm and Lyapunov exponents of random matrix systems. Further, we give complexity results about the execution time taken by the Sequential Probability Ratio Test.

Subject Classification

ACM Subject Classification
  • Theory of computation → Random walks and Markov chains
  • Mathematics of computing → Stochastic processes
  • Theory of computation → Logic and verification
  • Markov chains
  • hidden Markov models
  • probabilistic systems
  • verification


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