  The age of Incorrect Information (AoII) has been introduced recently to
address the shortcomings of the standard Age of information metric (AoI) in
real-time monitoring applications. In this paper, we consider the problem of
monitoring the states of remote sources that evolve according to a Markovian
Process. A central scheduler selects at each time slot which sources should
send their updates in such a way to minimize the Mean Age of Incorrect
Information (MAoII). The difficulty of the problem lies in the fact that the
scheduler cannot know the states of the sources before receiving the updates
and it has then to optimally balance the exploitation-exploration trade-off. We
show that the problem can be modeled as a partially Observable Markov Decision
Process Problem framework. We develop a new scheduling scheme based on
Whittle's index policy. The scheduling decision is made by updating a belief
value of the states of the sources, which is to the best of our knowledge has
not been considered before in the Age of Information area. To that extent, we
proceed by using the Lagrangian Relaxation Approach, and prove that the dual
problem has an optimal threshold policy. Building on that, we shown that the
problem is indexable and compute the expressions of the Whittle's indices.
Finally, we provide some numerical results to highlight the performance of our
derived policy compared to the classical AoI metric.
