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On the equivalence between standard and sequentially ordered hidden Markov models

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  • Chopin, N.

Abstract

Chopin [Chopin, N., 2007. Inference and model choice for sequentially ordered hidden markov models. J. R. Statist. Soc. B 69 (2), 269-284] introduced a sequentially ordered hidden Markov model, in which states are ordered according to their order of appearance, and claimed that such a model is a re-parametrisation of a standard Markov model. This note gives a formal proof that this equivalence holds in Bayesian terms, as both formulations generate equivalent posterior distributions, but does not hold in Frequentist terms, as both formulations generate incompatible likelihood functions. Perhaps surprisingly, this shows that Bayesian re-parametrisation and Frequentist re-parametrisation are not identical concepts.

Suggested Citation

  • Chopin, N., 2008. "On the equivalence between standard and sequentially ordered hidden Markov models," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2171-2174, October.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:14:p:2171-2174
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    1. Nicolas Chopin, 2007. "Inference and model choice for sequentially ordered hidden Markov models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 269-284, April.
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