The consistency of the BIC Markov order estimator

Imre Csiszár, Paul C. Shields

Research output: Contribution to journalArticle

5 Citations (Scopus)


We show that the BIC estimator of the order of a Markov chain (with finite alphabet) gives the correct order, eventually almost surely as the sample size goes to ∞, thereby strengthening earlier consistency results that assumed an apriori bound on the order. A key tool is a strong typicality result for Markov sample paths. We also show that the Bayesian or MDL estimator, of which the BIC estimator is regarded as an approximation, fails to be consistent for the uniformly distributed i.i.d. process.

Original languageEnglish
Number of pages1
JournalIEEE International Symposium on Information Theory - Proceedings
Publication statusPublished - Jan 1 2000

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modelling and Simulation
  • Applied Mathematics

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