  In this paper, a general value of information (VoI) framework is formalised
for latent variable models. In particular, the mutual information between the
current status at the source node and the observed noisy measurements at the
destination node is used to evaluate the information value, which gives the
theoretical interpretation of the reduction in uncertainty in the current
status given that we have measurements of the latent process. Moreover, the VoI
expression for a hidden Markov model is obtained in this setting. Numerical
results are provided to show the relationship between the VoI and the
traditional age of information (AoI) metric, and the VoI of Markov and hidden
Markov models are analysed for the particular case when the latent process is
an Ornstein-Uhlenbeck process. While the contributions of this work are
theoretical, the proposed VoI framework is general and useful in designing
wireless systems that support timely, but noisy, status updates in the physical
world.
