 Hello everyone, this is Alice Gao. In this video, I'm going to discuss the semantics or the meanings of Bayesian networks. There are two ways to interpret a Bayesian network. First, a Bayesian network represents a joint probability distribution. Given a Bayesian network, we have enough information to recover every probability in the joint distribution. Second, a Bayesian network encodes many conditional and unconditional independence relationships between the variables. Let's look at the first interpretation. How do we recover the joint probability distribution given a Bayesian network? We can use this formula. The formula denotes a product of many terms. There is one term for every node Xi in the network. Each term is the probability of the variable Xi conditioning on its parents. Let me show you one example of the calculation. After that, you can practice using another example. Let's calculate the probability of the following event. The alarm has sounded. There is no burglary and no earthquake. Both Dr. Watson and Mrs. Gibbon call and say that they hear the alarm. There is no radio report of an earthquake. There are lots of false alarms in this scenario. Nothing is happening, no burglary, no earthquake. Yet the alarm is sounding and both Watson and Gibbon are calling. What is the likelihood of this combination of events? Let's first write down the joint probability. Recall that we need one term for each node in the network. First, we have P0B since burglary has no parents. Next, we have P probability of not E since earthquake has no parents. Next, we have probability of A given not B and not E since alarm depends on B and E. After that, we have probability of not R given not E since radio depends on earthquake. Finally, we have probability of W given A and probability of G given A since Dr. Watson and Mrs. Gibbon both depend on alarm. After this, it's a matter of plugging numbers. Before I show you the answer, do you expect this probability to be large or small? Think about this for a bit and then keep watching. Here's the answer. The probability is quite small, which is a good thing. In our story, there are three noisy sensors. Alarm is a sensor for burglary and earthquake. Watson and Gibbons are sensors for alarm and radio is a sensor for earthquake. If these sensors are somewhat reliable, then the probability of having lots of false alarms should be small. Finally, this is a practice question for you. Calculate the joint probability when nothing interesting is happening in the world. Pause the video and solve this yourself. Then keep watching for the answer. The correct answer is A. Take a look at the calculations. The probability is quite large, which makes intuitive sense. Most of the time, nothing exciting is happening in the world. So that's why we say no news is good news. Before I end this video, let me give you another question to think about. Why does this formula make sense? So far, you can calculate the joint probability in two ways. One, using the chain rule and two, using the formula that I just described. Fix an order of the variables. On the left, write down the expression using the chain rule. And on the right, write down the expression using this formula. Then for each variable, compare the two corresponding terms. If the two corresponding terms are equal, what does it tell you? Can you infer an independence relationship involving the variable? I'll explain this in future videos. That's everything for this video. Let me summarize. After watching this video, you should be able to calculate any joint probability given a Bayesian network. Thank you very much for watching. I will see you in the next video. Bye for now.