Exact Computation of the Observed Information Matrix for Hidden Markov Models

This article describes a new algorithm for exact computation of the observed information matrix in hidden Markov models that may be performed in a single pass through the data. The score vector and log-likelihood are computed in the same pass. The new algorithm is derived from the forward–backward algorithm traditionally used to evaluate the likelihood in hidden Markov models. Our result is discussed in the context of previous approaches that have been used to obtain approximate standard errors of parameter estimates in these models. Implications for parameter estimation are also discussed. An application of the proposed methods to rainfall occurrence data is provided.