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Markov Models for Time Series Analysis

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Likelihood and Bayesian Inference

Part of the book series: Statistics for Biology and Health ((SBH))

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Abstract

A time series is a series of observations of a quantity of interest. Markov models are commonly used in applications to take into account the dependence between successive observations. This chapter describes the statistical analysis of different types of Markov models for categorical and continuous time series data, including hidden Markov models and state space models. Several examples are considered to illustrate how likelihood and Bayesian methods can be used for parameter estimation and prediction. Exercises are given at the end.

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References

  • Baum, L. E., Petrie, T., Soules, G. & Weiss, N. (1970). A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains. The Annals of Mathematical Statistics, 41, 164–171.

    Article  MathSciNet  Google Scholar 

  • Carlin, B. P. & Polson, N. G. (1992). Monte Carlo Bayesian methods for discrete regression models and categorical time series. In J. M. Bernardo, J. O. Berger, A. Dawid & A. Smith (Eds.), Bayesian Statistics 4 (pp. 577–586). Oxford: Oxford University Press.

    Google Scholar 

  • Chen, P.-L., Bernard, E. J. & Sen, P. K. (1999). A Markov chain model used in analyzing disease history applied to a stroke study. Journal of Applied Statistics, 26(4), 413–422.

    Article  Google Scholar 

  • Cox, D. R. (1981). Statistical analysis of time series. Some recent developments. Scandinavian Journal of Statistics, 8(2), 93–115.

    MathSciNet  MATH  Google Scholar 

  • Devroye, L. (1986). Non-uniform random variate generation. New York: Springer. Available at http://luc.devroye.org/rnbookindex.html.

    Book  Google Scholar 

  • Diggle, P. J. (1990). Time series: a biostatistical introduction. Oxford: Oxford University Press.

    MATH  Google Scholar 

  • Diggle, P. J., Heagerty, P. J., Liang, K.-Y. & Zeger, S. L. (2002). Analysis of longitudinal data (2nd ed.). Oxford: Oxford University Press.

    MATH  Google Scholar 

  • Grimmett, G., & Stirzaker, D. (2001). Probability and random processes (3rd ed.). Oxford: Oxford University Press.

    MATH  Google Scholar 

  • Reynolds, P. S. (1994). Time-series analyses of beaver body temperatures. In N. Lange, L. Ryan, D. Billard, L. Brillinger, L. Conquest & J. Greenhouse (Eds.), Case studies in biometry (pp. 211–228). New York: Wiley. Chap. 11.

    Google Scholar 

  • Shumway, R. H., & Stoffer, D. S. (2017). Time series analysis and its applications: with R examples (4th ed.). Cham: Springer International Publishing.

    Book  Google Scholar 

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Held, L., Sabanés Bové, D. (2020). Markov Models for Time Series Analysis. In: Likelihood and Bayesian Inference. Statistics for Biology and Health. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-60792-3_10

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