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

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  • Svetlana Ekisheva

    (Syktyvkar State University)

  • Mark Borodovsky

    (Georgia Institute of Technology)

Abstract

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.

Suggested Citation

  • Svetlana Ekisheva & Mark Borodovsky, 2011. "Uniform Accuracy of the Maximum Likelihood Estimates for Probabilistic Models of Biological Sequences," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 105-120, March.
    • Handle: RePEc:spr:metcap:v:13:y:2011:i:1:d:10.1007_s11009-009-9125-7
    DOI: 10.1007/s11009-009-9125-7
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    References listed on IDEAS

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    1. Glynn, Peter W. & Ormoneit, Dirk, 2002. "Hoeffding's inequality for uniformly ergodic Markov chains," Statistics & Probability Letters, Elsevier, vol. 56(2), pages 143-146, January.
    2. Roberts, G. O. & Tweedie, R. L., 1999. "Bounds on regeneration times and convergence rates for Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 80(2), pages 211-229, April.
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