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 […]

"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 […]

This is something I wrote about a decade ago, on my old website which no longer exists. I still like it, so I reproduce it here with some minor edits. What I am about to write should not really be necessary. I am certain that a satisfactory discussion of the subject exists elsewhere, and the […]