It seems to me that if you think in terms of likelihoods, you look at a story and say "but the converse of this story has high enough likelihood that we can't rule it out!" whereas if you think in terms of likelihood ratios, you say "it seems that this story is weakly more plausible than its converse."
I have several problems with this line of reasoning. First, I am unsure what it means for a story to be true. It's a story -- it arranges a set of facts in a pattern pleasing to the human brain. Not contradicting any known facts is a very low threshold (see the Russell's teapot), to call something "true" I'll need more than that and if a story makes no testable predictions I am not sure on which basis I should evaluate its truth and what does it even mean.
Second, it seems to me that in such situations the likelihoods and so, necessarily, their ratios are very very fuzzy. My meta uncertainty -- uncertainty about probabilities -- is quite high. I might say "story A is weakly more plausible than story B" but my confidence in my judgment about plausibility is very low. This judgment might not be worth anything.
Third, likelihood ratios are good when you know you have a complete set of potential explanations. And you generally don't. For open-ended problems the explanation "something else" frequently looks like the more plausible one, but again, the meta uncertainty is very high -- not only you don't know how uncertain you are, you don't even know what you are uncertain about! Nassim Taleb's black swans are precisely the beasties that appear out of "something else" to bite you in the ass.
First, I am unsure what it means for a story to be true.
Ah, by that I generally mean something like "the causal network N with a particular factorization F is the underlying causal representation of reality," and so a particular experiment measures data and then we calculate "the aforementioned causal network would generate this data with probability P" for various hypothesized causal networks.
For situations where you can control at least one of the nodes, it's easy to see how you can generate data useful for this. For situations whe...
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