The current state of my understanding (briefly):
- I very much understand reductionism and the distinction between the map and the territory. And I very much understand that probability is in the mind.
- From what I understand, prior probability is just the probability you thought something was going to happen before having observed some evidence, and posterior probability is just the probability you think something will happen after having observed that evidence.
- I don't really have a precise way of using evidence to update my beliefs though. I'm trying to think of and explain how I currently use evidence to update my beliefs, and I'm disappointed to say that I am struggling. I guess I just sort of think something along the lines of "I'd be unlikely that I observe X if A were really true. I observed X. I think it's less likely that A is true now."
- I've made attempts at learning Bayes' Theorm and stuff. When I think it through slowly, it makes sense. But it really takes me time to think it through. Without referring to explanations and thinking it through, I forget it. And I know that that demonstrates my lack of "true" understanding. In general, my short term memory and ability to reason through quantitative things quickly seems to be well above average, but far from elite. Probably way below average amongst this community.
I definitely plan on taking the time to study probability completely and from the ground up. I also plan on doing this for math in general, and a handful of other things as well.
- What are the practical benefits of having an intuitive understanding of Bayes' Theorem? If it helps, please name an example of how it impacted your day today.
- I mention in 3) that it takes me time to think it through. To those of you who consider yourselves to have an intuitive understanding, do you have to think it through, or do you instinctively update in a Bayesian way?
- How urgent is it to intuitively understand Bayesian thinking? To use me as an example, my short-mid-term goals include getting good at programming and starting a startup. I have a ways to go, and am working towards these things. So I spend most of my time learning programming right now. Is it worth me taking a few weeks/months to study probability?
I don't intend for this post to just be about me. I sense that other's have similar questions, and that this post would be a useful reference. So please keep this in mind and try to respond in such a way that would be useful to a wide audience. However, I do think that concrete examples would be useful here, and so responding to my particular situation would probably be useful to that wide audience.