I think that is what I had in mind, but it sounds from the way you’re saying it that this hasn’t been discussed as a specific technique for visualizing belief probabilities.
That surprises me since I’ve found it to be very useful, at least for intuitively getting a handle on my confidence in my own beliefs. When dealing with the question of what probability to assign to belief X, I don’t just give it a single probability estimate, and I don’t even give it a probability estimate with the qualifier that my confidence in that probability is low/moderate/high. Rather I visualize a graph with (usually) a bell curve peaking at the probability estimate I’d assign and whose width represents my certainty in that estimate. To me that’s a lot more nuanced than just saying “50% with low confidence”. It has also helped me to communicate to others what my views are for a given belief. I’d also suspect that you can do a lot of interesting things by mathematically manipulating and combining such graphs.
One problem is that it’s turtles all the way down.
What’s your confidence in your confidence probability estimate? You can represent that as another probability distribution (or another model, or a set of models). Rinse and repeat.
Another problem is that it’s hard to get reasonable estimates for all the curves that you want to mathematically manipulate. Of course you can wave hands and say that a particular curve exactly represents your beliefs and no one can say it ain’t so, but fake precision isn’t exactly useful.
I think that is what I had in mind, but it sounds from the way you’re saying it that this hasn’t been discussed as a specific technique for visualizing belief probabilities.
That surprises me since I’ve found it to be very useful, at least for intuitively getting a handle on my confidence in my own beliefs. When dealing with the question of what probability to assign to belief X, I don’t just give it a single probability estimate, and I don’t even give it a probability estimate with the qualifier that my confidence in that probability is low/moderate/high. Rather I visualize a graph with (usually) a bell curve peaking at the probability estimate I’d assign and whose width represents my certainty in that estimate. To me that’s a lot more nuanced than just saying “50% with low confidence”. It has also helped me to communicate to others what my views are for a given belief. I’d also suspect that you can do a lot of interesting things by mathematically manipulating and combining such graphs.
One problem is that it’s turtles all the way down.
What’s your confidence in your confidence probability estimate? You can represent that as another probability distribution (or another model, or a set of models). Rinse and repeat.
Another problem is that it’s hard to get reasonable estimates for all the curves that you want to mathematically manipulate. Of course you can wave hands and say that a particular curve exactly represents your beliefs and no one can say it ain’t so, but fake precision isn’t exactly useful.