Hierarchical Bayesian Estimation for Stationary Autoregressive Models Using Reversible Jump MCMC Algorithm

  • Authors

    • Supar man
    • Mohd Saifullah Rusiman
    2018-11-30
    https://doi.org/10.14419/ijet.v7i4.30.22007
  • Autoregressive model, Hierarchical Bayesian, Reversible jump MCMC

  • Abstract

    The autoregressive model is a mathematical model that is often used to model data in different areas of life. If the autoregressive model is matched against the data then the order and coefficients of the autoregressive model are unknown. This paper aims to estimate the order and coefficients of an autoregressive model based on data. The hierarchical Bayesian approach is used to estimate the order and coefficients of the autoregressive model. In the hierarchical Bayesian approach, the order and coefficients of the autoregressive model are assumed to have a prior distribution. The prior distribution is combined with the likelihood function to obtain a posterior distribution. The posterior distribution has a complex shape so that the Bayesian estimator is not analytically determined. The reversible jump Markov Chain Monte Carlo (MCMC) algorithm is proposed to obtain the Bayesian estimator. The performance of the algorithm is tested by using simulated data. The test results show that the algorithm can estimate the order and coefficients of the autoregressive model very well. Research can be further developed by comparing with other existing methods.

  • References

    1. [1] Okada K, Hando S, Teranishi M, Matsumoto Y & Fukumoto I (2001), Analysis of pathological tremors using the autoregression model. Frontiers Med. Biol. Engng 11(3), pp. 221-235.

      [2] Ramdane-Cherif Z, Nait-Ali A, Motsch JF & Krebs MO (2004), An autoregressive (AR) model applied to eye tremor movement, clinical application in Schizophrenia. Journal of Medical Systems, 28(5), pp. 489-495.

      [3] Kisi O (2005), Daily river forecasting using artificial neural networks and auto-regressive models. Turkish J. Eng. Env. Sci 29, pp. 9-20.

      [4] Zhao W, Morgan JT & Davis CE (2008), Gas chromatography data classification based on complex coefficients of an autoregressive model. Journal of sensors, pp. 1-9.

      [5] Lee J & Chon K H (2010), Respiratory rate extraction via an autoregressive model using the optimal parameter search criterion. Annals of Biomedical Engineering 38(10), pp. 3218-3225.

      [6] Figueiredo E & Figueiras J (2011), Influence of the autoregressive model order on damage detection. Computer-Aided Civil and Infrastructure Engineering 26, pp. 225-238.

      [7] Kim SH, Faloutsos C & Yang H-J (2013), Coercively adjusted autoregression model for forecasting in epilepsy. EEG Computational and Mathematical Methods in Medicine, pp 1-12.

      [8] Jayawardhana M, Zhu X, Liyanapathirana R & Gunawardana U (2015), Statistical damage sensitive feature for structural damage detection using AR model coefficients. Advances in Structural Engineering 18(10), pp. 1551-1562.

      [9] Zhang Y, Qi X & Li Q (2014), Simulation of dynamic light scattering based on AR model. Applied Mechanics and Materials 571-572, pp 840-844.

      [10] Zhao N, Yu F R, Sun H, Yin H, Nallanathan A & Wang G (2015), Interference alignment with delayed channel state information and dynamic AR-model channel prediction in wireless networks. Wireless Netw 21, pp. 1227-1242.

      [11] Dai X, Liu J & Zhang H (2015). Application of AR model in the analysis of pre-earthquake Ionospheric anomalies. Mathematical Problem in Engineering, pp. 157-184.

      [12] Yuewen Z, Yongjiu Z, Zhufeng L & Peng Z (2015), Prediction of ship main engine exhaust gas temperature using AR model. Applied Mechanics and Materials 697, pp. 244-248.

      [13] Song C (2016), Random signal frequency identification based on AR model spectral estimation. International Journal on Smart and Intelligent Systems 9(2).

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  • How to Cite

    man, S., & Saifullah Rusiman, M. (2018). Hierarchical Bayesian Estimation for Stationary Autoregressive Models Using Reversible Jump MCMC Algorithm. International Journal of Engineering & Technology, 7(4.30), 64-67. https://doi.org/10.14419/ijet.v7i4.30.22007

    Received date: 2018-11-28

    Accepted date: 2018-11-28

    Published date: 2018-11-30