Jaynes would emphasize background information I that provides the contextual information that allows a meaningful estimate. Without identifying and specifying that contextual information as something specific, the mind spins round and round on hypotheticals, and you will “notice that you are confused”.
I’ve found it helpful to specify that background knowledge, even if I’m not committed to it. Then do the math for alternatives scenarios as well. You can’t estimate until you narrow down reality enough to have some meaningful scenario where you can make causal inferences.
Another point Jaynes makes. You have to be very clear on what the facts are. Many “facts” are reports about facts by others, continuing a chains of artifacts, reports, and communications. Is the evidence the book you see in front of you, or the assumption that the reported historical and translational lineage of the the book in front of you is accurate back to the original author?
For example, you say
1) P(no crypt|no Julius Caesar) ~ 1.
P(no crypt|no Julius Caesar, All known reports on Caesar) is a very different animal than P(no crypt|no Julius Caesar, No known reports of a Julius Caesar exist). If you have a zillion reports on Caesar, and he didn’t exist, it would seem that someone did a good job pretending that he did exist. Wouldn’t they want make a pretend crypt too? Maybe not, but on balance, probably. This can be more causally circumscribed by I = All reported contemporaneous reports occurred.
A couple points.
Jaynes would emphasize background information I that provides the contextual information that allows a meaningful estimate. Without identifying and specifying that contextual information as something specific, the mind spins round and round on hypotheticals, and you will “notice that you are confused”.
I’ve found it helpful to specify that background knowledge, even if I’m not committed to it. Then do the math for alternatives scenarios as well. You can’t estimate until you narrow down reality enough to have some meaningful scenario where you can make causal inferences.
Another point Jaynes makes. You have to be very clear on what the facts are. Many “facts” are reports about facts by others, continuing a chains of artifacts, reports, and communications. Is the evidence the book you see in front of you, or the assumption that the reported historical and translational lineage of the the book in front of you is accurate back to the original author?
For example, you say
P(no crypt|no Julius Caesar, All known reports on Caesar) is a very different animal than P(no crypt|no Julius Caesar, No known reports of a Julius Caesar exist). If you have a zillion reports on Caesar, and he didn’t exist, it would seem that someone did a good job pretending that he did exist. Wouldn’t they want make a pretend crypt too? Maybe not, but on balance, probably. This can be more causally circumscribed by I = All reported contemporaneous reports occurred.