Bayesian Probability
Lots of thoughts going through my mind regarding Bayesian Probability. It started with an article I read in the Washington Post a few years ago about Frank Ramsey, an English mathematician, who wrote a paper in 1926 entitled "Truth and Probability." In May 2020, I read a review in the New Yorker of a Ramsey biography, "A Sheer Excess of Power" by Cheryl Misak. Ramsey was “... the first to define probability in terms of subjective degrees of belief. Belief was analogous to an individual’s memories or perception.” It goes back to what we were taught, experienced, or perceived as central to our beliefs. Our beliefs and previous experience create what Robert Pirsig, in "Zen and the Art of Motorcycle Maintenance," called "a prior" knowledge, which filters how people perceive the world and defines reality as a synthesis of elements from a fixed hierarchy of a priori concepts.
Bayes' Theorem provides a method for improving our belief system by the incremental addition of objective information. In "The Theory That Would Not Die" by Sharon Bertsch Mcgrayne regarding Bayes Theorem, the author writes: "By updating our initial belief about something with objective new information, we get a new and improved belief." So, somewhere in this line of thought, I came up with the idea that I could improve my decisions by improving my beliefs and hierarchy of prior concepts through Bayesian Probability. Now, the issue is to find out how to make improved beliefs operational by identifying my beliefs and challenging them with any new information I can find. The more systematic the approach, the better, but I wanted to start by examining outcomes to understand the basic methodology of Bayesian Probability. This led me to look at National Basketball Association (NBA) statistics for successful challenges by NBA coaches to defensive foul calls. You can find the outcome of every challenge for the NBA 2023 - 2024 season here.
NBA Coach's Challenges 2023 - 2024