Stupid Questions February 2017

Erfeyah

This thread is for asking any questions that might seem obvious, tangential, silly or what-have-you. Don't be shy, everyone has holes in their knowledge, though the fewer and the smaller we can make them, the better.

Please be respectful of other people's admitting ignorance and don't mock them for it, as they're doing a noble thing.

To any future monthly posters of SQ threads, please remember to add the "stupid_questions" tag.

Please be respectful of other people's admitting ignorance and don't mock them for it, as they're doing a noble thing.

To any future monthly posters of SQ threads, please remember to add the "stupid_questions" tag.

Ahhh, this is confusing me. I intuitively feel a 50-50 chance implies a uniform distribution. But what you are saying about the distribution being a spike for 0.5 makes total sense. Well, I guess I have a bit of studying to do...

I intuitively feel a 50-50 chance implies a uniform distribution

Well, imagine a bet on a fair coin flip. That's a 50-50 chance, right? And yet there is no uniform distribution in sight.

3gjm9y

Being a full-on Bayesian means not only having probability assignments for every proposition, but also having the conditional probabilities that will allow you to make appropriate updates to your probability assignments when new information comes in. The difference between "The probability of X is definitely 0.5" and "The probability of X is somewhere between 0 and 1, and I have no idea at all where" lies in how you will adjust your estimates for Pr(X) as new information comes in. If your estimate is based on a lot of strong evidence, then your conditional probabilities for X given modest quantities of new evidence will still be close to 0.5. If your estimate is a mere seat-of-the-pants guess, then your conditional probabilities for X given modest quantities of new evidence will be all over the place. Sometimes this is described in terms of your probability estimates for your probability estimates. That's appropriate when, e.g., what you know about X is that it is governed by some sort of random process that makes X happen with a particular probability (a coin toss, say) but you are uncertain about the details of that random process (e.g., does something about the coin or how it's tossed mean that Pr(heads) is far from 0.5?). But similar issues arise in different cases where there's nothing going on that could reasonably be called a random process but your degree of knowledge is greater or less, and I'm not sure the "probabilities of probabilities" perspective is particularly helpful there.