I assume you are pretty confident, as most people are. And with good reason, you have lived long enough to notice that when you go to sleep and wake up again the sun rises with you. When did you start to feel really confident of this ? After the 20th time? The 100th ? Or maybe you still think it is still fairly likely that it won’t rise again but you’re quite ready to accept whatever happens and confident that you’ll adapt. Or perhaps you’re more of a scientific purist where your confidence comes from knowing that the sun does not rise as much as we circle around it and so there’s a clear time threshold where you would reasonably expect the sun to rise again.
One of history’s greats, David Hume, was not so confident. He considered that it was no more rational to claim the sun would rise again than to assert that it would not.
How do you truly know that the sun will rise again? Well, you do not.
However, you can start to make some predictions based on prior probabilities, and then with a neat mathematical trick developed by another great, Thomas Bayes, you can now begin to live in a world we slowly approach a better understanding of the world. One not ruled by coin-flips but instead by the radical idea that the past is a pretty good indicator of what can happen in the future.
Here is how you can do it.
Estimate your prior probability for the event (x), find out what the likelihood of the event happening again is (y), and what the probability of it not happening again is (z). Finally, do some Bayesian mathematics:
The likelihood of the sun rising based on previous experience is very high, (x = 99.98%), the chance of the sun rising tomorrow if we accept Humes’ logic (y = 50%, z = 50%). Finally we do some maths and find the posterior probability and we find ourselves with 99.98%. Clearly the prior probability combined with the uncertainty essentially left us with our prior probability. So, this means we shouldn’t going around in an array of confusion about what could or could not happen, we can say a lot about what is likely in the world.
This concept is explored by Nate Silver where he talked about a different, more humorous example. Let’s say that you (female) come home after a work trip and find a pair of women’s underwear that are not yours. Let’s try and work out the likelihood that your husband is cheating on you. Nate starts with a prior probability of him cheating on you at 4% (x), he then consider the change of the underwear appearing if he is cheating on you to be 50% (y) and if he is not to be 5% (Z). There a whole range of plausible explanations that you have to consider here, for example, what if it’s a relative who stayed over, a pair of underwear that you forgot was yours, among many others. Finally, let’s add it all together and see what we get.
Using the aforementioned formula we find ourselves with 29% chance that your husband is having an affair which, whilst still very high, is not even probable.
There is some room for complaint here, why is the percentile so low ? Well, we do have a bias for new information, and this can totally uproot everything, including entire histories of behaviours. So we should prioritise prior probabilities as they are quite resilient in the fact of new evidence, as they give us a much more realistic picture of how likely certain events are.