I find the idea of having a range of probabilities sensible.
If you give a single probability, all you tell someone is your expectation of what will happen.
If you give a probability range you’re transmitting both your probability AND your certainty that your probabiliy is correct; IOW (In Other Words) you are telling the listener how much evidence you believe yourself to have.
So, as you gain more evidence your probability range will narrow.
When you find a probability through bayes-fu, you need a prior.
Precisely one prior.
Which is going to be pretty arbitrary.
But what if you picked two symmetrical priors, and applied the evidence to those?
You start with prior 1: 99.99%
Prior 2: 0.01%
When you have a reasonable amount of evidence you’ll find that prior 1 and prior 2 result in similar values (ie. prior 1 might give 40% while prior 2 gives 25%)
If you were to get more evidence, the difference would gradually vanish, and the smaller the probability range the more firm your probability is.
I find the idea of having a range of probabilities sensible.
If you give a single probability, all you tell someone is your expectation of what will happen.
If you give a probability range you’re transmitting both your probability AND your certainty that your probabiliy is correct; IOW (In Other Words) you are telling the listener how much evidence you believe yourself to have.
So, as you gain more evidence your probability range will narrow.
To clarify:
When you find a probability through bayes-fu, you need a prior. Precisely one prior. Which is going to be pretty arbitrary.
But what if you picked two symmetrical priors, and applied the evidence to those? You start with prior 1: 99.99% Prior 2: 0.01%
When you have a reasonable amount of evidence you’ll find that prior 1 and prior 2 result in similar values (ie. prior 1 might give 40% while prior 2 gives 25%) If you were to get more evidence, the difference would gradually vanish, and the smaller the probability range the more firm your probability is.