Bayesian Reasoning
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Bayesian statistics is all about making a prediction and updating it as you go, or about figuring out how likely something is given that something else is true or false.
For example, you have two coins in a bag. One is a regular coin with a heads and a tails. The other is a trick coin with two heads. You pull one coin out of the bag. How likely is it that you picked the real coin? Now, you flip it, and it comes up heads. *Now* how likely is it that you picked the real coin? Say you flip the same coin again and get heads again. Does the likelihood that you picked the real coin change?
Another way to think of it is like a game of Marco Polo. In case you’re not familiar, one person is blindfolded. They should “Marco” and the other person (or people) reply “Polo.” For now, let’s assume you and a friend are playing in a large room. You’re blindfolded, and your friend isn’t allowed to move. You stand in the centre of the room and shout. You hear your friend off to your left. But you’re not sure if they’re in front or behind you, or how far left. So you walk diagonally forwards to the left, half way to the corner of the room. Now you shout again. When your friend replies, you can tell if they’re still to your left (i.e. close to the wall) or if they’re now on your right (i.e. between where you are and the middle). You can also tell if they’re closer to you or further away, i.e. in the front of back half of the room. You keep moving about and shouting. Each time you build up a better picture of where your friend is. Each of these turns wouldn’t be very helpful by themselves, but together they give you a lot of information.
One of the main fields where Bayesian analysis gets used (whether consciously or not) is in medicine. Say there’s a really rare illness that maybe 1/100,000 people have. One of the symptoms is a cough. This means is you pick someone off the street at random, there’s only a 1/100,000 chance they have it. Now, you develop a cough. You go to the Drs and mention this condition. Is it likely that you have it? Probably not. It’s rare, and a cough is a common symptom of a lot of stuff. But you have a slightly higher than 1/100,000 chance. Now, let’s say you are ginger, and this illness is more common amongst ginger people. Well, the chances you’ve got it are higher. Also, there happens to be an outbreak in your area. It’s now beginning to look much more likely that you have this condition. So, each of these fact separately might make it seem unlikely that you had this illness. But together, we get a more accurate picture of what’s going on.
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