Approximating the variance of the conditional probability of the state of a hidden Markov Model

David O. Siegmund*, Benjamin Yakir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In a hidden Markov model, one "estimates" the state of the hidden Markov chain at t by computing via the forwards-backwards algorithm the conditional distribution of the state vector given the observed data. The covariance matrix of this conditional distribution measures the information lost by failure to observe directly the state of the hidden process. In the case where changes of state occur slowly relative to the speed at which information about the underlying state accumulates in the observed data, we compute approximately these covariances in terms of functionals of Brownian motion that arise in change-point analysis. Applications in gene mapping, where these covariances play a role in standardizing the score statistic and in evaluating the loss of noncentrality due to incomplete information, are discussed. Numerical examples illustrate the range of validity and limitations of our results.

Original languageAmerican English
Article number18
JournalStatistical Applications in Genetics and Molecular Biology
Issue number1
StatePublished - 6 Jul 2007

Bibliographical note

Funding Information:
KEYWORDS: gene mapping, noncentrality parameter, missing information, exponentiated Brownian motion Author Notes: This research has been partially supported by grants from the Israel-US Binational Science Foundation, the NSF, and the NIH.


  • Exponentiated Bownian motion
  • Gene mapping
  • Missing information
  • Noncentrality parameter


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