One of my favorite lessons from Bayesianism is that the task of calculating the probability of an event can be broken down into simpler calculations, so that even if you have no basis for assigning a number to P(H) you might still have success estimating the likelihood ratio.
Good question. I didn’t have an answer right away. I think it’s useful because it gives structure to the act of updating beliefs. When I encounter evidence for some H I immediately know to estimate P(E|H) and P(E|~H) and I know that this ratio alone determines the direction and degree of the update. Even if the numbers are vague and ad hoc this structure precludes a lot of clever arguing I could be doing, leads to productive lines of inquiry, and is immensely helpful for modeling my disagreement with others. Before reading LW I could have told you, if asked, that P(H), P(E|H), and P(E|~H) were worth considering; but becoming acutely aware that these are THE three quantities I need, no more and no less, has made a huge difference in my thinking for the better (not to sound dogmatic; I’ll use different paradigms when I think they’re more appropriate e.g. when doing math).
One of my favorite lessons from Bayesianism is that the task of calculating the probability of an event can be broken down into simpler calculations, so that even if you have no basis for assigning a number to P(H) you might still have success estimating the likelihood ratio.
How is that information by itself useful?
Good question. I didn’t have an answer right away. I think it’s useful because it gives structure to the act of updating beliefs. When I encounter evidence for some H I immediately know to estimate P(E|H) and P(E|~H) and I know that this ratio alone determines the direction and degree of the update. Even if the numbers are vague and ad hoc this structure precludes a lot of clever arguing I could be doing, leads to productive lines of inquiry, and is immensely helpful for modeling my disagreement with others. Before reading LW I could have told you, if asked, that P(H), P(E|H), and P(E|~H) were worth considering; but becoming acutely aware that these are THE three quantities I need, no more and no less, has made a huge difference in my thinking for the better (not to sound dogmatic; I’ll use different paradigms when I think they’re more appropriate e.g. when doing math).