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Related Experiment Videos

Confidence intervals for hidden Markov model parameters.

I Visser1, M E Raijmakers, P C Molenaar

  • 1Department of Psychology, University of Amsterdam, The Netherlands. op_visser@macmail.psy.uva.nl

The British Journal of Mathematical and Statistical Psychology
|December 8, 2000
PubMed
Summary

For long time series (T > 100), likelihood profiling and bootstrapping provide reliable confidence intervals (CIs) for hidden Markov model parameters. Finite-difference Hessian approximations yield CIs that are generally too small.

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Area of Science:

  • Statistics
  • Computational Statistics
  • Time Series Analysis

Background:

  • Hidden Markov models (HMMs) are widely used for analyzing sequential data.
  • Accurate confidence intervals (CIs) are crucial for parameter estimation in HMMs.
  • Computing CIs for HMMs with long time series presents computational challenges.

Purpose of the Study:

  • To compare three methods for computing confidence intervals (CIs) of hidden Markov model parameters.
  • To evaluate the feasibility of computing the exact Hessian for long time series.
  • To assess the performance of different interpolation methods for likelihood profiles.

Main Methods:

  • Comparison of three CI computation methods: likelihood profiling, bootstrapping, and finite-differences approximation of the Hessian.

Related Experiment Videos

  • Simulation studies using long time series (T > 100).
  • Evaluation of quadratic and cubic interpolation polynomials for likelihood profiles.

    • Main Results:

    • Computing the exact Hessian is computationally infeasible for long time series.
    • Likelihood profiling and bootstrapping yield comparable CIs.
    • CIs derived from the finite-differences approximation of the Hessian tend to be underestimated.

    Conclusions:

    • Likelihood profiling and bootstrapping are recommended for computing CIs in HMMs with long time series.
    • The finite-differences approximation of the Hessian is not suitable for this context.
    • Further research can explore optimized interpolation techniques for likelihood profiles.