 Hello, everyone. This is Alice Gao. In this video, I'm going to explain the second example on constructing a Bayesian network. This is an example on slide 47 in lecture 11. In this example, we have the network where we have W and G being noisy sensors of A, and then we're changing the order and trying to construct another correct Bayesian network. And the correct order we are going to use is the order we're going to use is W first, then G, then A. Based on the given order, we are going to add the nodes to the network one by one, and each time we add a node, we are going to look at the existing nodes and choose the minimum set of parents from the existing nodes such that the new node is conditionally independent of all the other existing nodes given the parents. Step one, adding the first node never is always really easy. No work to do. Step two, we need to add the second node to the network. First of all, we need to think about W is already there. So can we add G with a parent set of size zero? Well, we can do this if G is independent from W. Let's look at the original network. Well, in the original network, G and W are not independent. They actually influence each other through A. So since G is not independent from W, we cannot add it with no parents. So the only other possibility is that we will add G and choose W to be the only parent of G. Step number three, let's add A to the network. We already have W and G, and when we're adding A, we can first think about can we add A with no parent again? Well, if we want to add A with no parent, then we need to verify whether A is independent from G and whether A is independent from W. If both are true, then we can add A with no parent. Is this the case? Of course not. Look at the original network. A and W are connected, so A and W are not independent, and A and G are also connected, so they're not independent as well. Which means too bad. We cannot add A with no parents. Let's try to add A with only one parent. See if that works. Which means can we make W the only parent of A, or can we make G the only parent of A? Well, if we want to make W the only parent of A, then we need to verify that A is conditionally independent of G given W. Is this the case in our original network? Of course not. If we know W, A and G are still connected, they still influence each other. So given W, A and G are not independent. Similarly, given G, A and W are not independent either. If we know the value of G, A and W are still directly connected, so they're still going to directly influence each other. So unfortunately, we cannot choose a parent set of size one as well. So the only remaining possibility is that we have to choose both W and G to be parents of A. And this is how we got our final correct answer for the Bayesian network. Notice something interesting in the Bayesian network. Remember that when we're discussing this structure, I told you that W and G are not unconditionally independent. So they're unconditionally dependent on each other. And this alternative network actually makes that relationship explicit. It there is explicitly an edge between W and G telling you that if one of them changes, then the other one would change. So they're dependent on each other. So this relationship was implicit in our original network, but by changing the order of the variables, it becomes explicit in this new network. That's everything for this video. Thank you for watching, and I will see you in the next one. Bye for now.