Eliezer: The distinction between direct observation and deduction is pretty ambiguous for a Bayesian, is it not?
Um… not at all, actually. A key insight into causal networks consists of giving prior-probability messages and likelihood-evidential messages two separate pathways to travel along, and recombining the two only after the messages have propagated separately. Like counting soldiers in a line using a distributed algorithm by having each soldier report the number of soldiers behind (and passing that number + 1 forward) and having each soldier report the number of soldiers forward (and passing that number + 1 behind) and only recombining the two messages afterward, rather than mixing them up as they pass.
So you will generally want a very crisp distinction between your reasons to believe something because of what you believe about its generating process, and your reasons to believe something because of what you have observed of its effects.
Eliezer: The distinction between direct observation and deduction is pretty ambiguous for a Bayesian, is it not?
Um… not at all, actually. A key insight into causal networks consists of giving prior-probability messages and likelihood-evidential messages two separate pathways to travel along, and recombining the two only after the messages have propagated separately. Like counting soldiers in a line using a distributed algorithm by having each soldier report the number of soldiers behind (and passing that number + 1 forward) and having each soldier report the number of soldiers forward (and passing that number + 1 behind) and only recombining the two messages afterward, rather than mixing them up as they pass.
So you will generally want a very crisp distinction between your reasons to believe something because of what you believe about its generating process, and your reasons to believe something because of what you have observed of its effects.