So when I said “rain is the correct inference to make”, you somehow read that as “P(rain) = 1″? Because I see no other explanation why you felt the need to write entire paragraphs about what probabilities and priors are. I even explicitly mentioned priors in my comment, just to prevent a reply just like yours, but apparently that wasn’t enough.
Characterizing this as “A implies C, but (A ∧ B) does not imply C” is tendentious in the extreme (not to mention so gross a simplification that it can hardly be evaluated as coherent view).
Ok. How do you think I should have explained the situation? Preferably, in less than four paragraphs?
I personally find my explanation completely clear, especially since I expected most people to be familiar with the sidewalk/rain/sprinkler example, or something similar. But then I’m aware that my judgements about clarity don’t always match other people’s, so I’ll try to take your advice seriously.
How do you think I should have explained the situation? Preferably, in less than four paragraphs?
Assuming that “the situation” in question is this, from upthread—
We unfortunately live in a world where sometimes A implies C, but A & B does not imply C, for some values of A, B, C.
I would state the nearest-true-claim thus:
“Sometimes P(C|A) is very low but P(C|A,B) is much higher, enough to make it the dominant conclusion.”
Edit: Er, I got that backwards, obviously. Corrected version:
“Sometimes P(C|A) is very high, enough to make it the dominant conclusion, but P(C|A,B) is much lower [this is due to the low prior probability of B but the high conditional probability P(C|B)]”.
Ok, that’s reasonable. At least I understand why you would find such explanation better.
One issue is that I worry about using the conditional probability notation. I suspect that sometimes people are unwilling to parse it. Also the “very low” and “much higher” are awkward to say. I’d much prefer something in colloquial terms.
Another issue, I worry that this is not less confusing. This is evidenced by you confusing yourself about it, twice (no, P(C|B), or P(rain|sprinkler) is not high, and it doesn’t even have to be that low). I think, ultimately, listing which probabilities are “high” and which are “low” is not helpful, there should be a more general way to express the idea.
Zulupineapple do you release you have been engaged in a highly decoupled argument?
Your point (made way back) that values contextual conclusions is valid but decoupling is needed to enhance those conclusions and as it is harder by an order of magnitude requires more practice and knowledge.
Personally I feel the terms abstract and concrete are more useful. Alternating between the two and refining the abstract ideas before applying them to concrete examples.
So when I said “rain is the correct inference to make”, you somehow read that as “P(rain) = 1″? Because I see no other explanation why you felt the need to write entire paragraphs about what probabilities and priors are. I even explicitly mentioned priors in my comment, just to prevent a reply just like yours, but apparently that wasn’t enough.
Ok. How do you think I should have explained the situation? Preferably, in less than four paragraphs?
I personally find my explanation completely clear, especially since I expected most people to be familiar with the sidewalk/rain/sprinkler example, or something similar. But then I’m aware that my judgements about clarity don’t always match other people’s, so I’ll try to take your advice seriously.
Assuming that “the situation” in question is this, from upthread—
I would state the nearest-true-claim thus:
“Sometimes P(C|A) is very low but P(C|A,B) is much higher, enough to make it the dominant conclusion.”
Edit: Er, I got that backwards, obviously. Corrected version:
“Sometimes P(C|A) is very high, enough to make it the dominant conclusion, but P(C|A,B) is much lower [this is due to the low prior probability of B but the high conditional probability P(C|B)]”.
Ok, that’s reasonable. At least I understand why you would find such explanation better.
One issue is that I worry about using the conditional probability notation. I suspect that sometimes people are unwilling to parse it. Also the “very low” and “much higher” are awkward to say. I’d much prefer something in colloquial terms.
Another issue, I worry that this is not less confusing. This is evidenced by you confusing yourself about it, twice (no, P(C|B), or P(rain|sprinkler) is not high, and it doesn’t even have to be that low). I think, ultimately, listing which probabilities are “high” and which are “low” is not helpful, there should be a more general way to express the idea.
Zulupineapple do you release you have been engaged in a highly decoupled argument? Your point (made way back) that values contextual conclusions is valid but decoupling is needed to enhance those conclusions and as it is harder by an order of magnitude requires more practice and knowledge.
Personally I feel the terms abstract and concrete are more useful. Alternating between the two and refining the abstract ideas before applying them to concrete examples.