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Parameter redundancy and identifiability in hidden Markov models

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  • Diana J. Cole

    (University of Kent)

Abstract

Hidden Markov models are a flexible class of models that can be used to describe time series data which depends on an unobservable Markov process. As with any complex model, it is not always obvious whether all the parameters are identifiable, or if the model is parameter redundant; that is, the model can be reparameterised in terms of a smaller number of parameters. This paper considers different methods for detecting parameter redundancy and identifiability in hidden Markov models. We examine both numerical methods and methods that involve symbolic algebra. These symbolic methods require a unique representation of a model, known as an exhaustive summary. We provide an exhaustive summary for hidden Markov models and show how it can be used to investigate identifiability.

Suggested Citation

  • Diana J. Cole, 2019. "Parameter redundancy and identifiability in hidden Markov models," METRON, Springer;Sapienza Università di Roma, vol. 77(2), pages 105-118, August.
    • Handle: RePEc:spr:metron:v:77:y:2019:i:2:d:10.1007_s40300-019-00156-3
    DOI: 10.1007/s40300-019-00156-3
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    References listed on IDEAS

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    Cited by:

    1. Jan Bulla & Roland Langrock & Antonello Maruotti, 2019. "Guest editor’s introduction to the special issue on “Hidden Markov Models: Theory and Applications”," METRON, Springer;Sapienza Università di Roma, vol. 77(2), pages 63-66, August.
    2. J. W. Smith & L. R. Johnson & R. Q. Thomas, 2023. "Assessing Ecosystem State Space Models: Identifiability and Estimation," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(3), pages 442-465, September.
    3. MacDonald, Iain L., 2020. "A coarse-grained Markov chain is a hidden Markov model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).

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