Efficient Bayesian estimation and use of cut posterior in semiparametric hidden Markov models
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...
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| Format: | Journal article |
| Language: | English |
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Institute of Mathematical Statistics
2024
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| _version_ | 1824458837635104768 |
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| author | Moss, D Rousseau, J |
| author_facet | Moss, D Rousseau, J |
| author_sort | Moss, D |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2025-02-19T04:32:14Z |
| format | Journal article |
| id | oxford-uuid:d8262a45-4ad5-4cea-b648-216049ff71a5 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2025-02-19T04:32:14Z |
| publishDate | 2024 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | oxford-uuid:d8262a45-4ad5-4cea-b648-216049ff71a52025-01-13T12:41:33ZEfficient Bayesian estimation and use of cut posterior in semiparametric hidden Markov modelsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:d8262a45-4ad5-4cea-b648-216049ff71a5EnglishSymplectic ElementsInstitute of Mathematical Statistics2024Moss, DRousseau, JWe 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. |
| spellingShingle | Moss, D Rousseau, J Efficient Bayesian estimation and use of cut posterior in semiparametric hidden Markov models |
| title | Efficient Bayesian estimation and use of cut posterior in semiparametric hidden Markov models |
| title_full | Efficient Bayesian estimation and use of cut posterior in semiparametric hidden Markov models |
| title_fullStr | Efficient Bayesian estimation and use of cut posterior in semiparametric hidden Markov models |
| title_full_unstemmed | Efficient Bayesian estimation and use of cut posterior in semiparametric hidden Markov models |
| title_short | Efficient Bayesian estimation and use of cut posterior in semiparametric hidden Markov models |
| title_sort | efficient bayesian estimation and use of cut posterior in semiparametric hidden markov models |
| work_keys_str_mv | AT mossd efficientbayesianestimationanduseofcutposteriorinsemiparametrichiddenmarkovmodels AT rousseauj efficientbayesianestimationanduseofcutposteriorinsemiparametrichiddenmarkovmodels |