Now, just to make sure I got it, does this make sense: the question of gods existence (assuming the term was perfectly defined) is a yes/no question but you are conceptualising the probability that a yes or a no is true. That is why you are using a uniform distribution in a question with a binary answer. It is not representing the answer but your current confidence. Right?
Skipping a complicated discussion about many meanings of “probability”, yes.
Think about it this way. Someone gives you a box and says that if you press a button, the box will show you either a dragon head or a dragon tail. That’s all the information you have.
What’s the probability of the box showing you a head if you press the button? You don’t know. This means you need an estimate. If you’re forced to produce a single-number estimate (a “point estimate”) it will be 50%. However if you can produce this estimate as a distribution, it will be uniform from 0 to 1. Basically, you are very unsure about your estimate.
Now, let’s say you had this box for a while and pressed the button a couple thousands of times. Your tally is 1017 heads and 983 tails. What is your point estimate now? More or less the same, rounding to 50%. But the distribution is very different now. You are much more confident about your estimate.
Your probability estimate is basically a forecast of what do you think will happen when you press the button. Like with any forecast, there is a confidence interval around it. It can be wide or it can be narrow.
You are obviously right! This is helpful :)
Now, just to make sure I got it, does this make sense: the question of gods existence (assuming the term was perfectly defined) is a yes/no question but you are conceptualising the probability that a yes or a no is true. That is why you are using a uniform distribution in a question with a binary answer. It is not representing the answer but your current confidence. Right?
Skipping a complicated discussion about many meanings of “probability”, yes.
Think about it this way. Someone gives you a box and says that if you press a button, the box will show you either a dragon head or a dragon tail. That’s all the information you have.
What’s the probability of the box showing you a head if you press the button? You don’t know. This means you need an estimate. If you’re forced to produce a single-number estimate (a “point estimate”) it will be 50%. However if you can produce this estimate as a distribution, it will be uniform from 0 to 1. Basically, you are very unsure about your estimate.
Now, let’s say you had this box for a while and pressed the button a couple thousands of times. Your tally is 1017 heads and 983 tails. What is your point estimate now? More or less the same, rounding to 50%. But the distribution is very different now. You are much more confident about your estimate.
Your probability estimate is basically a forecast of what do you think will happen when you press the button. Like with any forecast, there is a confidence interval around it. It can be wide or it can be narrow.