 Hello everyone, this is Alice Gao. In this video, I will discuss the sensor model for our umbrella story. By sensors, I mean the noisy signal we observe about the state at each time step. The signal on a day is true if the director carries an umbrella and falls otherwise. The signal at time t correspond to the evidence variable O sub t. The value of O sub t could potentially depend on all the states as sub zero up to S sub t and all the previous signals. O sub zero up to O sub t minus one. As you can see, we will encounter a similar problem as before. The conditional probability distribution will grow unboundedly as time goes on. Let's make another Markov assumption for the signals. To distinguish this from the Markov assumption regarding the states, let's call it the sensor Markov assumption. The sensor Markov assumption says that each state has sufficient information to generate its observations. Therefore, O sub t needs to condition on S sub t only. We can simplify the conditional probability to the probability of O sub t given S sub t. Similar to the transition model, we will assume that the sensor model is stationary. That is, the sensor model for every time step remains the same. This is the complete hidden Markov model for the umbrella story. Let me use this example to describe some important components of a hidden Markov model. They're also described in words on the next slide. First, the variables. The state at each time step is not observable, but the state generates a noisy signal that's observable. Second, the state transition satisfies the Markov assumption. Each state depends on the previous state only. Also, the sensor model satisfies the Markov assumption as well. Each observation depends on the current state only. In addition, we simplified our umbrella model by making some further assumptions. We assumed that the state transitions are stationary. The transition probabilities at each time step are the same. We also assumed that the sensor model is stationary. The probabilities of generating a signal at each time step are the same. That's everything on the hidden Markov model for the umbrella story. Let me summarize. After watching this video, you should be able to do the following. Define a sensor model for the umbrella story. Describe the complete hidden Markov model for the umbrella story. Describe important components of a hidden Markov model. Why is it hidden and why is it Markov? Thank you very much for watching. I will see you in the next video. Bye for now.