HiddenMarkov-package {HiddenMarkov}

Overview of Package HiddenMarkov

Description

In this topic we give an overview of the package.

Classes of Hidden Markov Models Analysed

The classes of models currently fitted by the package are listed below. Each are defined within an object that contains the data, current parameter values, and other model characteristics.

Discrete Time Hidden Markov Model:

is described under the topic dthmm. This model can be simulated or fitted to data by defining the required model structure within an object of class "dthmm".

Markov Modulated Generalised Linear Model:

is described under the topic mmglm1.

Markov Modulated Generalised Linear Longitudinal Model:

is described under the topic mmglmlong1.

Markov Modulated Poisson Process:

is described under the topic mmpp. This model can be simulated or fitted to data by defining the required model structure within an object of class "mmpp".

Main Tasks Performed by the Package

The main tasks performed by the package are listed below. These can be achieved by calling the appropriate generic function.

Simulation of HMMs:

can be performed by the function simulate.

Parameter Estimation:

can be performed by the functions BaumWelch (EM algorithm), or neglogLik together with nlm or optim (Newton type methods or grid searches).

Model Residuals:

can be extracted with the function residuals.

Model Summary:

can be extracted with the function summary.

Log-Likelihood:

can be calculated with the function logLik.

Prediction of the Markov States:

can be performed by the function Viterbi.

All other functions in the package are called from within the above generic functions, and only need to be used if their output is specifically required. We have referred to some of these other functions as “2nd level” functions, for example see the topic mmpp-2nd-level-functions.

Organisation of Topics in the Package

Cited References:

anywhere in the manual are only listed within this topic.

General Documentation:

topics summarising general structure are indexed under the keyword “documentation” in the Index.

Acknowledgement

Many of the functions contained in the package are based on those of Walter Zucchini (2005).

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. Annals of Mathematical Statistics 41(1), 164–171. doi: 10.1214/aoms/1177697196

Charnes, A.; Frome, E.L. & Yu, P.L. (1976). The equivalence of generalized least squares and maximum likelihood estimates in the exponential family. J. American Statist. Assoc. 71(353), 169–171. doi: 10.2307/2285762

Dempster, A.P.; Laird, N.M. & Rubin, D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion). J. Royal Statist. Society B 39(1), 1–38. URL: https://www.jstor.org/stable/2984875

Elliott, R.J.; Aggoun, L. & Moore, J.B. (1994). Hidden Markov Models: Estimation and Control. Springer-Verlag, New York. doi: 10.1007/978-0-387-84854-9

Harte, D. (2019). Mathematical Background Notes for Package “HiddenMarkov”. Statistics Research Associates, Wellington. URL: https://www.statsresearch.co.nz/dsh/sslib/manuals/notes.pdf

Hartley, H.O. (1958). Maximum likelihood estimation from incomplete data. Biometrics 14(2), 174–194. doi: 10.2307/2527783

Klemm, A.; Lindemann, C. & Lohmann, M. (2003). Modeling IP traffic using the batch Markovian arrival process. Performance Evaluation 54(2), 149–173. doi: 10.1016/S0166-5316(03)00067-1

MacDonald, I.L. & Zucchini, W. (1997). Hidden Markov and Other Models for Discrete-valued Time Series. Chapman and Hall/CRC, Boca Raton.

McCullagh, P. & Nelder, J.A. (1989). Generalized Linear Models (2nd Edition). Chapman and Hall, London.

Rabiner, L.R. (1989). A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of the IEEE 77(2), 257–286. doi: 10.1109/5.18626

Roberts, W.J.J.; Ephraim, Y. & Dieguez, E. (2006). On Ryden's EM algorithm for estimating MMPPs. IEEE Signal Processing Letters 13(6), 373–376. doi: 10.1109/LSP.2006.871709

Ryden, T. (1994). Parameter estimation for Markov modulated Poisson processes. Stochastic Models 10(4), 795–829. doi: 10.1080/15326349408807323

Ryden, T. (1996). An EM algorithm for estimation in Markov-modulated Poisson processes. Computational Statistics & Data Analysis 21(4), 431–447. doi: 10.1016/0167-9473(95)00025-9

Zucchini, W. (2005). Hidden Markov Models Short Course, 3–4 April 2005. Macquarie University, Sydney.