Baye’s Theorem considers “Priors” (also called “signals”) – events that we have pre-existing knowledge on – and “Posteriors” – events that we want to predict. While the theorem has again been around for over 250 years, well-known journalist Nate Silver has adapted the theorem into what he calls the “Bayesian convergence,” or the method of dispelling myths and opposing opinions as evidence of the most likely outcome is uncovered.
As in our previous articles, our subject of focus will be the concept, marketability, or point of attraction behind Baye’s Theorem. Specifically, how Nate approaches it different from others, so much so that he is now assembling a team to carry out his approach to journalism as part of the relaunch of his site, FiveThirtyEight.com.
But in order for his findings, and those under him, to be statistically accurate, even the most unique journalist pieces need to be based on what Baye’s Theorem calls “Priors.” But while the result is to dispel myths, these disruptive results need to be based on prior statistical findings.
First, this is the example that Wikipedia uses to explain Baye’s Theroem (you can read the equation part here:
Suppose a man told you he had had a nice conversation with someone on the train. Not knowing anything about this conversation, the probability that he was speaking to a woman is 50% (assuming the train had an equal number of men and women and the speaker was as likely to strike up a conversation with a man as with a woman). Now suppose he also told you that his conversational partner had long hair. It is now more likely he was speaking to a woman, since women are more likely to have long hair than men. Bayes’ theorem can be used to calculate the probability that the person was a woman.
A Game of Priors The first finding, gained as the result of corresponding Nate’s work to the sefirah of chochmah, is that the primary task of a past-minded predictive journalist should be to continuously weigh and reanalyze Priors (pre-existing statistic) not Posteriors (event we want to predict).
For events that already occurred, as in the train example, instead of searching for the most probable Posterior, the approach of chochmah, the yiddishe kop, is to search for the one true Anterior (what actually happened).
As we will explain later, Nate still has come up with a good chap (catch) with how he approaches Baye’s Theorem for events that have not yet occurred. But for the meantime, since most examples used to explain Baye’s describe events that happened, these relate to an exercise in discovering the one true outcome, not the most probable.
This story aptly illustrates this point. Appropriately enough, another train story! (reprinted with permission from Jewlarious.com):
After months of negotiation with the authorities, a Talmudist from Odessa was finally granted permission to visit Moscow.
He boarded the train and found an empty seat. At the next stop, a young man got on and sat next to him. The scholar looked at the young man and he thought: This fellow doesn’t look like a peasant, so if he is no peasant he probably comes from this district. If he comes from this district, then he must be Jewish because this is, after all, a Jewish district.
But on the other hand, since he is a Jew, where could he be going? I’m the only Jew in our district who has permission to travel to Moscow.
Ahh, wait! Just outside Moscow there is a little village called Samvet, and Jews don’t need special permission to go to Samvet But why would he travel to Samvet? He is surely going to visit one of the Jewish families there. But how many Jewish families are there in Samvet? Aha, only two — the Bernsteins and the Steinbergs. But since the Bernsteins are a terrible family, so such a nice looking fellow like him, he must be visiting the Steinbergs.