The most interesting book I've read lately is Chivers' "Everything is Predictable", about the universality of Bayes' Theorem and how it applies to every aspect of science, even the decision making of humans. It turns out that our brains are just as logical as the scientific method, which tests a hypothesis by weighing it against prior data and updating the probability that something will happen in a given set of parameters. Bayes' Theorem takes the obvious prior information when frequentism doesn't, presenting a rift in statistical theory. Frequentism simply measures the probability that something will happen in a given sample without any prior data.
Modern science has become like mining- mining for data, that is. Why we use frequentism in modern science instead of Bayesian statistics is beyond me. It has helped me realize that science and academia are industries like everything else. Frequentism allows this kind of ruthless publishing whose sole purpose is to ask for more funding. Real science that involves Bayes' Theorem applies prior probabilities to new information.
With Bayesian statistics, we realized that knowledge is only a spectrum of what is probable, not what is fact or fiction. Reality is merely the probability that an event will occur given prior conditions, which we test with our brains all the time. In fact, as creatures of reason, it is the principal way we learn to adjust our behavior in the world. The next time you make a decision, think about all the prior information you used to weigh the probability of it being correct or incorrect. It's enough to blow your mind.
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