Approximating the Variance of the Conditional Probability of the State of a Hidden Markov Model

Siegmund David O and Yakir Benjamin
Additional contact information
Siegmund David O: Stanford University
Yakir Benjamin: The Hebrew University of Jerusalem

Statistical Applications in Genetics and Molecular Biology, 2007, vol. 6, issue 1, 21

Abstract: 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.

Keywords: gene mapping; noncentrality parameter; missing information; exponentiated Brownian motion (search for similar items in EconPapers)
Date: 2007
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.2202/1544-6115.1296 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:sagmbi:v:6:y:2007:i:1:n:18

Ordering information: This journal article can be ordered from
https://www.degruyter.com/view/j/sagmb

DOI: 10.2202/1544-6115.1296

Access Statistics for this article

Statistical Applications in Genetics and Molecular Biology is currently edited by Michael P. H. Stumpf

More articles in Statistical Applications in Genetics and Molecular Biology from De Gruyter
Bibliographic data for series maintained by Peter Golla ().