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This article starts off with a common mistake. It is ok to create the 3 categories: > If I suspect that A→B, and I collect data and establish beyond doubt tha

by dj-wonk 12y ago

This article starts off with a common mistake. It is ok to create the 3 categories: > If I suspect that A→B, and I collect data and establish beyond doubt that A&B correlates r=0.7, how much evidence do I have that A→B? > you can divvy up the possibilities as: 1. A causes B 2. B causes A 3. both A and B are caused by a C So far so good, but here is the problem: > Even if we were guessing at random, you’d expect us to be right (at at least 33% of the time... No. It is not valid to assume each possibility is equally likely. If you do so, you are bringing your own assumptions to the problem. If you ever find yourself assuming a distribution, pause and consider testing your assumption.

Jemaclus 12y ago
If you read the whole article, he addresses this about halfway down.
- dj-wonk 12y ago
  @Jemaclus I'm not sure why you assumed that I did not read the article. Maybe you disagreed with my conclusion and assumed I had not read the article? To your question, I would ask: Where, exactly, does the author "address this"? (Maybe we are talking about different meaning of "this"? I explain the fallacy I'm talking about in a longer comment on a sister thread (by "sister" I mean up one level, over one, down one). Did you mean this part? > It turns out, we weren’t supposed to be reasoning ‘there are 3 categories of possible relationships, so we start with 33%’, but rather: ‘there is only one explanation “A causes B”, only one explanation “B causes A”, but there are many explanations of the form “C1 causes A and B”, “C2 causes A and B”, “C3 causes A and B”…’, and the more nodes in a field’s true causal networks (psychology or biology vs physics, say), the bigger this last category will be. This is also fallacious, in my opinion. See my longer comment. In short, if you "count up" categories in this way, you are assuming information that you don't have; doing so is a matter of belief, not analysis. Or did you mean this part? > they might not be reasoning in a causal-net framework at all, but starting from the naive 33% base-rate you get when you treat all 3 kinds of causal relationships equally. > This could be shown by eliciting estimates and seeing whether the estimates tend to look like base rates of 33% and modifications thereof. This chunk of text does not debunk the claim that a 33% base rate is reasonable as a starting point. My point is that the 33% starting point was not reasonable in the first place.
jerf 12y ago
First, keep reading. Second, when gwern says "you'd expect 33%", he [1] does not mean "the abstract 'we' mathematically expect 33%", but indeed "the generic person-on-the-street has an intuitive belief that we should get 33%". If you check the context I think you'll see this fits. [1] So far as I know, anyhow.
- dj-wonk 12y ago
  @jerf Why did you assume I did not read the article? I read it, and I find the writing to be unclear. Maybe "you'd expect" means what you think; maybe not. Independent of my or your opinion, (or precisely because reasonable people may disagree over something so simple) the writing is unnecessarily unclear. It would be simple to add a quick note saying, more-or-less, that the author will revisit the point later. I also disagree with another commenter who says that the later writing clears up this issue. The point about 33% not being a fair assumption isn't addressed head on in the way that I think matters most. Here is my main point, which was not received in the spirit I intended. Many smart people, even programmers, sometimes incorrectly assume a discrete uniform distribution (e.g. 1/3, 1/3, 1/3 in the above example), probably because they think it makes the fewest assumptions. I'll put it another way with a related example. Alexa gives Bart a two-sided coin, tells him it may or not be fair, and asks the expected probability of getting heads. Bart reasons as follows: "I know that the coin may be unfair, ranging from, say, 0%/100% to 50%/50% to 100%/0%. By symmetry, for each 1%/99% coin there is a 99%/1% coin. So, in the end, the coin will average out to 50/50, so the best answer is 50%." Chuck comes along and says, "Bart got it wrong. Any point estimate must be incorrect, because we don't have enough information. The correct answer must be a distribution. Since we know nothing, the best answer is a flat (uniform) distribution ranging from 0% to 100%." Danielle chimes in and adds "Yes, Bart was wrong, and Chuck improved on the analysis, but Chuck did not go far enough. Both Bart and Chuck assumed symmetry, without justification. Chuck's act of assuming a uniform distribution is tantamount to knowing the process that generated the coin. Does Chuck really know the chances of a 0-10% coin are the same as a 10-20% coin, and so on? No, he does not. Therefore, even answering the question with a distribution is incorrect. The only correct answer is that the probability of heads ranges from 0 to 100%, but no distribution can be given." Danielle is correct. The author may well know this, but it is not communicated clearly in the article. I would be willing to wager that many people, when confronted with Alex's question, would answer like Bob or Chuck did.

by dj-wonk 12y ago

Jemaclus 12y ago

If you read the whole article, he addresses this about halfway down.

dj-wonk 12y ago
@Jemaclus I'm not sure why you assumed that I did not read the article. Maybe you disagreed with my conclusion and assumed I had not read the article? To your question, I would ask: Where, exactly, does the author "address this"? (Maybe we are talking about different meaning of "this"? I explain the fallacy I'm talking about in a longer comment on a sister thread (by "sister" I mean up one level, over one, down one). Did you mean this part? > It turns out, we weren’t supposed to be reasoning ‘there are 3 categories of possible relationships, so we start with 33%’, but rather: ‘there is only one explanation “A causes B”, only one explanation “B causes A”, but there are many explanations of the form “C1 causes A and B”, “C2 causes A and B”, “C3 causes A and B”…’, and the more nodes in a field’s true causal networks (psychology or biology vs physics, say), the bigger this last category will be. This is also fallacious, in my opinion. See my longer comment. In short, if you "count up" categories in this way, you are assuming information that you don't have; doing so is a matter of belief, not analysis. Or did you mean this part? > they might not be reasoning in a causal-net framework at all, but starting from the naive 33% base-rate you get when you treat all 3 kinds of causal relationships equally. > This could be shown by eliciting estimates and seeing whether the estimates tend to look like base rates of 33% and modifications thereof. This chunk of text does not debunk the claim that a 33% base rate is reasonable as a starting point. My point is that the 33% starting point was not reasonable in the first place.

jerf 12y ago

First, keep reading. Second, when gwern says "you'd expect 33%", he [1] does not mean "the abstract 'we' mathematically expect 33%", but indeed "the generic person-on-the-street has an intuitive belief that we should get 33%". If you check the context I think you'll see this fits. [1] So far as I know, anyhow.

dj-wonk 12y ago
@jerf Why did you assume I did not read the article? I read it, and I find the writing to be unclear. Maybe "you'd expect" means what you think; maybe not. Independent of my or your opinion, (or precisely because reasonable people may disagree over something so simple) the writing is unnecessarily unclear. It would be simple to add a quick note saying, more-or-less, that the author will revisit the point later. I also disagree with another commenter who says that the later writing clears up this issue. The point about 33% not being a fair assumption isn't addressed head on in the way that I think matters most. Here is my main point, which was not received in the spirit I intended. Many smart people, even programmers, sometimes incorrectly assume a discrete uniform distribution (e.g. 1/3, 1/3, 1/3 in the above example), probably because they think it makes the fewest assumptions. I'll put it another way with a related example. Alexa gives Bart a two-sided coin, tells him it may or not be fair, and asks the expected probability of getting heads. Bart reasons as follows: "I know that the coin may be unfair, ranging from, say, 0%/100% to 50%/50% to 100%/0%. By symmetry, for each 1%/99% coin there is a 99%/1% coin. So, in the end, the coin will average out to 50/50, so the best answer is 50%." Chuck comes along and says, "Bart got it wrong. Any point estimate must be incorrect, because we don't have enough information. The correct answer must be a distribution. Since we know nothing, the best answer is a flat (uniform) distribution ranging from 0% to 100%." Danielle chimes in and adds "Yes, Bart was wrong, and Chuck improved on the analysis, but Chuck did not go far enough. Both Bart and Chuck assumed symmetry, without justification. Chuck's act of assuming a uniform distribution is tantamount to knowing the process that generated the coin. Does Chuck really know the chances of a 0-10% coin are the same as a 10-20% coin, and so on? No, he does not. Therefore, even answering the question with a distribution is incorrect. The only correct answer is that the probability of heads ranges from 0 to 100%, but no distribution can be given." Danielle is correct. The author may well know this, but it is not communicated clearly in the article. I would be willing to wager that many people, when confronted with Alex's question, would answer like Bob or Chuck did.