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arXiv · 2606.02118

Observed Fisher Information in hidden Markov models - Application to a noisy Gaussian random walk

Alexandra Lefebvre·Grégory Nuel
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Abstract

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.

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Alexandra Lefebvre, Grégory Nuel. 2026-06-01. Observed Fisher Information in hidden Markov models - Application to a noisy Gaussian random walk. https://arxiv.org/abs/2606.02118

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