 Hello everyone, this is AliceGal. In this video, I will discuss how we can model a changing world using hidden Markov models. So far, we have looked at algorithms for reasoning in a static world, however, the real world changes over time. When the world changes, we need to reason about a sequence of events. In this video, I will introduce hidden Markov models and describe how we can use hidden Markov models to model a changing world. Hidden Markov models have many real world applications. There are a few examples on this slide. I will use an umbrella story as a running example. Here's the story. You are a security guard stationed at a secret underground installation. Every day, you want to know whether it's raining or not. Unfortunately, your only access to the outside world is when you see the director brings or does not bring an umbrella each morning. The story is a bit depressing, but it has some important elements. We're underground, but we want to know whether it's raining or not. The state of the world is whether it's raining or not, and we cannot observe the state directly. Instead, we will observe a signal whether the director comes with an umbrella or not. The signal tells us some information about the state of the world. Also, the signal is noisy since we are in a world with uncertainty. Even if it's raining, the director might not carry an umbrella because they forgot. Or when it's not raining, the director might carry an umbrella because they forgot to check the weather report. In short, the state is not observable, but we observe a noisy signal which tells us something about the state. Let's model the umbrella story using a Bayesian network. We need to reason about events over time. Let's define the time steps. For the umbrella story, a day is a reasonable time step. Every day, we observe a new signal and we may want to update our estimate of the state. Next, let's define some random variables. We need two types of random variables. First, we need to model the state, whether it's raining or not. Let's define a binary random variable s to denote the state. s is true when it's raining and false otherwise. We also need to model our noisy signal or observation. Let's define a binary random variable o to denote the signal or the observation. o is true when the director brings an umbrella and false otherwise. Note that I used the subscripts to indicate the time step for each variable. That's everything for this video. Let me summarize. After watching this video, you should be able to describe the variables for the umbrella story. Thank you very much for watching. I will see you in the next video. Bye for now.