A note on the application of the Oakes' identity to obtain the observed information matrix of hidden Markov models

TL;DR

This paper introduces a simplified method for deriving the observed information matrix of hidden Markov models using Oakes' identity, requiring only first derivatives of forward-backward recursions, demonstrated on a sociological dataset.

Contribution

It presents a novel approach that reduces computational complexity by avoiding second derivatives in the derivation of the observed information matrix for hidden Markov models.

Findings

The method simplifies calculations of the observed information matrix.

Application to a sociological dataset demonstrates practical utility.

The approach is computationally more efficient than previous methods.

Abstract

We derive the observed information matrix of hidden Markov models by the application of the Oakes (1999)'s identity. The method only requires the first derivative of the forward-backward recursions of Baum and Welch (1970), instead of the second derivative of the forward recursion, which is required within the approach of Lystig and Hughes (2002). The method is illustrated by an example based on the analysis of a longitudinal dataset which is well known in sociology.