Observed Fisher Information in hidden Markov models - Application to a noisy Gaussian random walk
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914622895816704 |
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| author | Lefebvre, Alexandra Nuel, Grégory |
| author_facet | Lefebvre, Alexandra Nuel, Grégory |
| contents | In this work we provide analytical and closed-form expressions for the exact computation of the score and the observed Fisher information matrix in a Gaussian random walk observed through Gaussian noise. Our method is based on the Oakes' identity and, as for the computation of the log-likelihood, its complexity in time is linear in the length of the sequence with the forward-backward (or Baum-Welch) algorithm. We illustrate the method over various simulation studies and provide parameter estimates computed with the Newton-Raphson algorithm along with confidence intervals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_02118 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Observed Fisher Information in hidden Markov models - Application to a noisy Gaussian random walk Lefebvre, Alexandra Nuel, Grégory Computation In this work we provide analytical and closed-form expressions for the exact computation of the score and the observed Fisher information matrix in a Gaussian random walk observed through Gaussian noise. Our method is based on the Oakes' identity and, as for the computation of the log-likelihood, its complexity in time is linear in the length of the sequence with the forward-backward (or Baum-Welch) algorithm. We illustrate the method over various simulation studies and provide parameter estimates computed with the Newton-Raphson algorithm along with confidence intervals. |
| title | Observed Fisher Information in hidden Markov models - Application to a noisy Gaussian random walk |
| topic | Computation |
| url | https://arxiv.org/abs/2606.02118 |