Open Access
2024 Efficient Bayesian estimation and use of cut posterior in semiparametric hidden Markov models
Daniel Moss, Judith Rousseau
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Electron. J. Statist. 18(1): 1815-1886 (2024). DOI: 10.1214/23-EJS2201


We consider the problem of estimation in Hidden Markov models with finite state space and nonparametric emission distributions. Efficient estimators for the transition matrix are exhibited, and a semiparametric Bernstein-von Mises result is deduced. Following from this, we propose a modular approach using the cut posterior to jointly estimate the transition matrix and the emission densities. We first derive a general theorem on contraction rates for this approach. We then show how this result may be applied to obtain a contraction rate result for the emission densities in our setting; a key intermediate step is an inversion inequality relating L1 distance between the marginal densities to L1 distance between the emissions. Finally, a contraction result for the smoothing probabilities is shown, which avoids the common approach of sample splitting. Simulations are provided which demonstrate both the theory and the ease of its implementation.


The project leading to this work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 834175). The project is also partially funded by the EPSRC via the CDT StatML.


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Daniel Moss. Judith Rousseau. "Efficient Bayesian estimation and use of cut posterior in semiparametric hidden Markov models." Electron. J. Statist. 18 (1) 1815 - 1886, 2024.


Received: 1 June 2022; Published: 2024
First available in Project Euclid: 22 April 2024

Digital Object Identifier: 10.1214/23-EJS2201

Keywords: Bernstein-von Mises , contraction rates , cut posterior , efficiency , Hidden Markov models , inversion inequality , Semiparametric estimation

Vol.18 • No. 1 • 2024
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