🤖 AI Summary
This study addresses the efficient and exact computation of the score function and observed Fisher information matrix in a Gaussian hidden Markov model (HMM) with Gaussian observation noise, where the latent state follows a Gaussian random walk. Leveraging Oakes’ identity in conjunction with the forward–backward algorithm, the authors derive, for the first time, a closed-form analytical expression for the observed Fisher information matrix and achieve linear-time exact computation of both the score function and the information matrix. This approach substantially enhances the efficiency and statistical accuracy of parameter estimation and enables rapid construction of confidence intervals. Experimental results across multiple simulated scenarios demonstrate that the proposed method reliably and efficiently performs parameter estimation, confirming its theoretical advantages and practical utility.
📝 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.