Have you read the last several posts? In those posts we began the tale of Alice and Bob, a pair of murder suspects who recently started dating one another. Through their sordid tale, we'll examine Bayesian reasoning, the scientific method, and the so-called fallacy of "affirming the consequent". Alice and Bob are going through a […]

In my last post, I introduced Bayes' theorem: P(hypothesis|observation) = P(observation|hypothesis)/P(observation) * P(hypothesis) Now, this is a powerful equation that tells us how to use observed evidence to update our beliefs about a hypothesis. But as I mentioned, it has two difficulties with its use: first, the probability prior to the observation - P(hypothesis) - […]

In my previous post, I explained that instead of thinking of logical statements as only being "true" or "false", we should assign probability values for their chance of being true. This is the fundamental tenet of Bayesian reasoning. This allows us to employ the entire mathematical field of probability theory in our thinking and expands […]

What is Bayesian inference? I've already mentioned it in several of my previous posts, and I'm sure to bring it up again in the future. I obviously think it's important. Why? Bayesian inference is the mathematical extension of propositional logic using probability theory. It is superior to deductive propositional logic, which is what many people […]

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"Proof" is one of those words that are abused nearly to the point of meaninglessness. I generally only use it in math-related contexts. I prefer the word "evidence" over "proof". So, instead of saying "This test score proves you didn't do your homework", I'd rather say "This test score is evidence that you didn't do […]

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