Uniform Accuracy of the Maximum Likelihood Estimates for Probabilistic Models of Biological Sequences

  • Svetlana Ekisheva
  • Mark BorodovskyEmail author


Probabilistic models for biological sequences (DNA and proteins) have many useful applications in bioinformatics. Normally, the values of parameters of these models have to be estimated from empirical data. However, even for the most common estimates, the maximum likelihood (ML) estimates, properties have not been completely explored. Here we assess the uniform accuracy of the ML estimates for models of several types: the independence model, the Markov chain and the hidden Markov model (HMM). Particularly, we derive rates of decay of the maximum estimation error by employing the measure concentration as well as the Gaussian approximation, and compare these rates.


Maximum likelihood estimate Asymptotic properties of estimates Hidden Markov model Concentration of measure 

AMS 2000 Subject Classifications

62M05 60J10 62F10 11L07 


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of MathematicsSyktyvkar State UniversitySyktyvkarRussia
  2. 2.Wallace H. Coulter Department of Biomedical Engineering and Computational Science and Engineering DivisionGeorgia Institute of TechnologyAtlantaUSA

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