We announce two results on the problem of estimating the order of a Markov chain from observation of a sample path. First is that the Bayesian Information Criterion (BIC) leads to an almost surely consistent estimator. Second is that the Bayesian minimum description length estimator, of which the BIC estimator is an approximation, fails to be consistent for the uniformly distributed i.i.d. process. A key tool is a strong ratio-typicality result for empirical k-block distributions. Complete proofs are given in the authors' article to appear in The Annals of Statistics.
|Number of pages||5|
|Journal||Electronic Research Announcements of the American Mathematical Society|
|Publication status||Published - Oct 19 1999|
- Bayesian information criterion
- Markov chains
- Order estimation
ASJC Scopus subject areas