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Probability & Statistics for Machine Learning & Data Science
33h26m
Now, this is something I mentioned before, but let me formalize it. We have something called the prior. That is the original probability that you can calculate not knowing anything else. Then something happens, and that's the event. The event gives you information about the probability. And with that information, you can calculate something called the posterior. So we had that the prior was P of A. An event can be called E. And the posterior is P of A given E. Now let me give you some examples. In the spam email, the prior was 20%. The prior was the number of spam emails divided by the total number of emails. The only thing I know about an email, if I know nothing else, is that it has a 20% probability of being spam because I know how many emails are spam in total. That is a very basic unit of information, and I need to know a little more. So we come up with a condition, an event. It says that the email contains the word lottery. So now the posterior changes. Now the probability that the email is spam given that it contains the word lottery is no longer the number of spam emails divided by the total number of emails, but it's now the number of spam emails with the word lottery divided by the total number of emails with the word lottery. And that's a much better probability. That's a much more accurate probability. So the posterior is always a better estimation than the prior because we have that event that gave us information. In the medical example, there was also a prior, an event, and a posterior. The prior was the original probability of being sick. The event is the fact that it diagnosed positive, and the posterior was the probability that you were sick given that you diagnosed positive. Now let's look at another example. Let's say you're rolling two dice, and you want to find the probability that the sum of the values is 10. We know that that's 3 divided by 36. Now if the event says that the first dice is a 6, then all of a sudden your posterior changes. It's 1 6 because you live in a different space. So that is the posterior. And in another example, the coin example, if you want to find the probability that both coins land in heads, then that's 1 quarter. But the event says that the first coin landed in heads. Therefore, in the posterior, you no longer have the second row, and the new probability is 1 half.