Giving a range of probabilities when you should give a probability + giving confidence intervals over probabilities + failing to realize that probabilities of probabilities just reduce to simple probabilities
This is just straightforwardly correct statistics. For example, ask a true bayesian to estimate the outcome of flipping a coin of unknown bias, and they will construct a probability distribution of coin flip probabilites, and only reduce this to a single probability when forced to make a bet. But when not taking a bet, they should be doing updates on the distribution, not the final estimate. (I’m pretty sure this is in fact the only logical way to do a bayesian update for the problem).
And why are we stating probabilities anyway? The main reason seems to be to quantify and communicate our beliefs. But if my “25% probability ” comes from a different distribution to your “25% probability ”, we may appear to be in agreement when in fact our worldviews differ wildly. I think giving credence intervals over probabilities is strictly better than this.
This is just straightforwardly correct statistics. For example, ask a true bayesian to estimate the outcome of flipping a coin of unknown bias, and they will construct a probability distribution of coin flip probabilites, and only reduce this to a single probability when forced to make a bet. But when not taking a bet, they should be doing updates on the distribution, not the final estimate. (I’m pretty sure this is in fact the only logical way to do a bayesian update for the problem).
And why are we stating probabilities anyway? The main reason seems to be to quantify and communicate our beliefs. But if my “25% probability ” comes from a different distribution to your “25% probability ”, we may appear to be in agreement when in fact our worldviews differ wildly. I think giving credence intervals over probabilities is strictly better than this.
Thanks. I agree! (Except with your last sentence.) Sorry for failing to communicate clearly; we were thinking about different contexts.