So far in this book, we have worked with observable variables, such as prices or quantities. But what happens when we have an unobserved variable? Let's suppose that we observe the number of people that walk over a street that has an underground station. This variable can, in principle, be modeled as a Poisson random variable (since it is count data). The number of people walking over this street depends on many variables, among them whether the station is open or closed. Let's further assume that we don't observe whether the station is open or not. We want to estimate whether the station is open or not based on the number of people that we observe. 

It's tempting to model the station status based on the amount of people walking, possibly using logistic regression or any other tool. The problem is that our dependent variable cannot be observed! Hidden Markov models (HMMs) assume that there is an unobserved variable that governs how the dependent variable behaves; in particular, it assumes that the unobserved state behaves according to a Markov chain (each state probability depends only on the previous state). For example, in our subway example, we assume that there exists a matrix that governs the transition from open to closed. Let's suppose that the rows reflect the current state and the columns reflect the next state: for example, cell (1,1) reflects the probability that an open station today remains open tomorrow, and cell (1,2) reflects the probability that an open station gets closed: