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Hidden Markov models with binary dependence

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  • Danisman, Ozgur
  • Uzunoglu Kocer, Umay

Abstract

Hidden Markov models are widely used to model the probabilistic structures with latent variables. The main assumption of hidden Markov models is that; observation symbols are conditionally independent and identically distributed random variables. There exist some cases where this assumption may not be valid in practice. That is, an observation symbol that occurs in the current state may depend on the previous observation symbol that occurred in the previous state. In this study, a new type of hidden Markov model is introduced in which the current pair of hidden state-emitted observation symbol and the previous pair of those have a first-order Markov dependency. The proposed model is capable of capturing a possible first-order Markov dependency between the last and the previous steps of the system. In addition, it provides a better representation for the appropriate real-life problems where, if the observation symbols have conditional dependence. It is an alternative model to the classical hidden Markov model for revealing the Markov dependency between the current and the previous binary information of the system. An experimental study is conducted to show the performance of the proposed model compared to the classical hidden Markov model. Besides, two different case studies are conducted namely the occurrences of strong earthquakes and daily stock prices are modeled with both the classical hidden Markov model and the proposed model, and the results are compared.

Suggested Citation

  • Danisman, Ozgur & Uzunoglu Kocer, Umay, 2021. "Hidden Markov models with binary dependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    • Handle: RePEc:eee:phsmap:v:567:y:2021:i:c:s0378437120309663
    DOI: 10.1016/j.physa.2020.125668
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    References listed on IDEAS

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    1. Enrique E. Alvarez, 2005. "Estimation in Stationary Markov Renewal Processes, with Application to Earthquake Forecasting in Turkey," Methodology and Computing in Applied Probability, Springer, vol. 7(1), pages 119-130, March.
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    Cited by:

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    3. Gámiz, M.L. & Navas-Gómez, F. & Raya-Miranda, R. & Segovia-García, M.C., 2023. "Dynamic reliability and sensitivity analysis based on HMM models with Markovian signal process," Reliability Engineering and System Safety, Elsevier, vol. 239(C).

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