If you haven’t already, you might want to take a look at Bayes Theorem by Eliezer.
As sort of a quick tip about where you might be getting confused: you summarize the steps involved as (1) come up with a prior, (2) identify potential evidence, and (3) update on the evidence. You’re missing one step. You also need to check to see whether the potential evidence is “true,” and you need to do that before you update.
If you check out Conservation of Expected Evidence, linked above, you’ll see why. You can’t update just because you’ve thought of some facts that might bear on your hypothesis and guessed at their probability—if your intuition is good enough, your guess about the probability of the facts that bear on the hypothesis should already be factored into your very first prior. What you need to do is go out and actually gather information about those facts, and then update on that new information.
For example: I feel hot. I bet I’m running a fever. I estimate my chance of having a bacterial infection that would show up on a microscope slide at 20%.
I think: if my temperature were above 103 degrees, I would be twice as likely to have a bacterial infection, and if my temperature were below 103 degrees, I would only be half as likely to have a bacterial infection. Considering how hot I feel, I guess there’s a 50-50 chance my temperature is above 103 degrees. I STILL estimate my chance of having a bacterial infection at 20%, because I already accounted for all of this. This is just a longhand way of guessing.
Now, I take my temperature with a thermometer. The readout says 104 degrees. Now I update on the evidence; now I think the odds that I have a bacterial infection are 40%.
The math is fudged very heavily, but hopefully it clarifies the concepts. If you want accurate math, you can read Eliezer’s post.
If you haven’t already, you might want to take a look at Bayes Theorem by Eliezer.
As sort of a quick tip about where you might be getting confused: you summarize the steps involved as (1) come up with a prior, (2) identify potential evidence, and (3) update on the evidence. You’re missing one step. You also need to check to see whether the potential evidence is “true,” and you need to do that before you update.
If you check out Conservation of Expected Evidence, linked above, you’ll see why. You can’t update just because you’ve thought of some facts that might bear on your hypothesis and guessed at their probability—if your intuition is good enough, your guess about the probability of the facts that bear on the hypothesis should already be factored into your very first prior. What you need to do is go out and actually gather information about those facts, and then update on that new information.
For example: I feel hot. I bet I’m running a fever. I estimate my chance of having a bacterial infection that would show up on a microscope slide at 20%.
I think: if my temperature were above 103 degrees, I would be twice as likely to have a bacterial infection, and if my temperature were below 103 degrees, I would only be half as likely to have a bacterial infection. Considering how hot I feel, I guess there’s a 50-50 chance my temperature is above 103 degrees. I STILL estimate my chance of having a bacterial infection at 20%, because I already accounted for all of this. This is just a longhand way of guessing.
Now, I take my temperature with a thermometer. The readout says 104 degrees. Now I update on the evidence; now I think the odds that I have a bacterial infection are 40%.
The math is fudged very heavily, but hopefully it clarifies the concepts. If you want accurate math, you can read Eliezer’s post.