 Hello everyone, this is Alice Gao. In this video, I'm going to talk about the third example on constructing a Bayesian network. This example is on slide 48 in lecture 11. In this example, we have a network with B, E, and A, where B and E jointly cause A to happen. And we want to construct an alternative correct network where we're using a different order. So A comes first, then B and E. Let's follow the steps of constructing a Bayesian network. For each step, based on the ordering, we will add the node to the network, then we'll decide on the parent set for the node. And we need to choose the parent set to be the smallest set such that this new node is conditionally independent from all other existing nodes given the parents. Step one, we want to add the first node to the network. Add it, we're done. Step two, we are trying to add B to the network. We already have A in the network, so we need to choose a set of parents for B. The smallest size for the parent set could be zero. So let's ask ourselves this question. If we want to choose no parent for B, we have to make sure that B is independent from A. Is this the case? Well, look at our original network. Nope, this is not the case. A and B are directly connected, so they're definitely not independent. So therefore, we cannot choose no parent for B. Well, the only other possibility is that we add B and choose A to be the only parent for B. Step number three, now we want to add E to the network. We already have A and B in the network, so we have a few possibilities here. First of all, let's try a parent set of size zero, which means no parent for E. If that's the case, we need to verify that E is independent from B and also E is independent from A. Is that the case? Well, let's look at our original network. B and E are indeed independent, but B and A are not independent. So E is not independent from both B and E, which means we cannot choose no parent for E. So this structure doesn't work. So the minimum size of zero for the parent set does not work. Let's try a size of one. So that means either we choose A to be the only parent for E, or we choose B to be the only parent for E. Does either of these work? Let's see. If we want to choose A to be the only parent for E, then we have to verify that E is independent of B given A. Is this the case? Well, for this network, one key property that I discussed is that given A, B and E become dependent. So they actually become related to each other if A is observed. This is the explaining away effect. So definitely given A, B and E are not independent. This doesn't work. Alternatively, given B are A and E independent. While knowing B, A and E are still directly connected, so they're not independent. Unfortunately, a parent set of size one also doesn't work. So the only possibility left is that we need to choose A and B to both be parents of E. This gives us the correct answer that I talked about in the previous video. Finally, notice something interesting in the network that I derived here. In the original network, one key property that I tried to explain is the fact that given A, B and E are not independent. They are actually related to each other. But the original network cannot represent this relationship explicitly because we added B and E first. And then we added A afterwards. However, in this new network, because we added B and E after A. So we have this extra link, which explicitly represent the relationship that given A, B and E are related from each other. They are not independent from each other. So this is an interesting observation that when we change the order in which we add the variables to the network, sometimes some implicit relationships in the network becomes explicit. That's everything for this video. Thank you very much for watching. I will see you in the next one. Bye for now.