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Maximum likelihood estimation of aggregated Markov processes

F Qin1, A Auerbach, F Sachs

  • 1Department of Biophysical Sciences, State University of New York at Buffalo 14214, USA.

Proceedings. Biological Sciences
|March 22, 1997
PubMed
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We developed a new maximum likelihood method for modeling aggregated Markov processes using dwell time sequences. This approach efficiently computes likelihoods and their derivatives, offering a stable and rapid solution for complex modeling tasks.

Area of Science:

  • Computational Statistics
  • Stochastic Processes
  • Mathematical Modeling

Background:

  • Aggregated Markov processes are widely used but challenging to model.
  • Existing methods may lack efficiency or numerical stability.
  • Accurate modeling is crucial for analyzing complex systems.

Purpose of the Study:

  • To introduce a novel maximum likelihood method for modeling aggregated Markov processes.
  • To develop an efficient computational procedure for likelihood and derivative calculation.
  • To demonstrate the method's numerical stability and rapid convergence.

Main Methods:

  • Utilized the joint probability density of observed dwell time sequences as the likelihood function.
  • Developed a forward-backward recursive procedure for efficient computation of likelihood and its derivatives.

Related Experiment Videos

  • Employed a variable metric optimizer for navigating the likelihood space.

    • Main Results:

    • Derived analytical formulae for the derivatives of the likelihood function.
    • The proposed method exhibits rapid convergence.
    • The method demonstrates numerical stability in computations.

    Conclusions:

    • The presented maximum likelihood method provides an effective and stable approach for modeling aggregated Markov processes.
    • The efficient computational procedures facilitate practical application.
    • Numerical examples confirm the method's effectiveness.