Still revising, but I figured that in true Bayesian fashion, I’d update this dynamically as more information came in
We come to understand most things when they are connected to the things that we already know. In an effort to better understand Bayes theorem’s meaning relative to frequentist interpretations, I’m reading about the history of its development.
The world was a different place back then. The very concept of ’cause and effect’ was politically charged in a way that would be difficult to imagine today. The basic issue was that people had, until recently, considered the immediate cause of everything to be God’s will. That’s why you could impress people so much by predicting an eclipse – it wasn’t that you were smart, it’s that you had an inside line to God. (Nate Silver would have done quite well back then). This may help explain how the prediction of Halley’s Comet was huge, because Halley didn’t claim that a divine connection allowed his accurate forecast of a highly improbable event. He laid out all the mathematics, and showed that natural laws were the cause. Suddenly, a whole class of celestial events were no longer the direct result of heavenly handiwork, but of predictable natural laws. The boundaries of God’s will, which had previous enveloped the observable reality in an all-encompassing embrace, began to recede.
Early experimentation focused on situations where one or two causes repeatedly led to an effect. If you did the same experimental steps (cause) again, you’d get pretty much the exact same result (effect). That’s awesome when it works, but there are plenty of situations in which the flow is:
Major Cause (consistently repeated many times) + many minor causes (randomly repeated many times) = Range of Effects (semi-randomly distributed)
Fortunately, those many random minor causes could sometimes be modelled as a probability distribution that was as stable as the gravitational constant. That’s where statistics comes in – creating that model of those minor causes, so that we can come as close as possible to a consisteny link between the Major Cause and Range of Effects.
That’s where Bayes comes in, and why his work had political importance – in a world where people were freaking out about the first few steps towards a mechanical universe, he created tools that would allow for a dramatically larger set of effects to be predicted and explained without appeal to a higher power.