Journal of Applied Probability

Fitting hidden semi-Markov models to breakpoint rainfall data

John Sansom and Peter Thomson

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The paper proposes a hidden semi-Markov model for breakpoint rainfall data that consist of both the times at which rain-rate changes and the steady rates between such changes. The model builds on and extends the seminal work of Ferguson (1980) on variable duration models for speech. For the rainfall data the observations are modelled as mixtures of log-normal distributions within unobserved states where the states evolve in time according to a semi-Markov process. For the latter, parametric forms need to be specified for the state transition probabilities and dwell-time distributions. Recursions for constructing the likelihood are developed and the EM algorithm used to fit the parameters of the model. The choice of dwell-time distribution is discussed with a mixture of distributions over disjoint domains providing a flexible alternative. The methods are also extended to deal with censored data. An application of the model to a large-scale bivariate dataset of breakpoint rainfall measurements at Wellington, New Zealand, is discussed.

Article information

J. Appl. Probab. Volume 38A, Issue (2001), 142-157.

First available in Project Euclid: 25 May 2004

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M05: Markov processes: estimation
Secondary: 86A10: Meteorology and atmospheric physics [See also 76Bxx, 76E20, 76N15, 76Q05, 76Rxx, 76U05]

Hidden semi-Markov models high-resolution rainfall data dwell-time distributions EM algorithm


Sansom, John; Thomson, Peter. Fitting hidden semi-Markov models to breakpoint rainfall data. J. Appl. Probab. 38A (2001), 142--157. doi:10.1239/jap/1085496598.

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