3 ms·

I've recently come to believe that Taleb really doesn't understand probability. I know this sounds like some insane flippant remark, but I saw a video where he

I've recently come to believe that Taleb really doesn't understand probability. I know this sounds like some insane flippant remark, but I saw a video where he talked about the election forecast as a martingale bounded between 0 and 1 and then made some claims about variance with these bounds to back up his claim against Silver. For his claim to make sense you would have to view probabilities as linear, which is not simply not how probabilities work. An event that has a 0.01 chance of happening is an order of magnitude more likely than one that has as 0.001 chance. However the different between and 0.5 and 0.501 is essentially negligible (hence probability is not linear because 0.001 does not mean the same everywhere). I've generally given Taleb a pass as a bit of a crank that doesn't care about the philosophical interpretation of probability, but after seeing him misunderstand probability in such a major way I've started writing him off entirely. edit: I should add I'm not particularly more convinced that Silver really understands all that much either, just that this is all two very loud people that don't know much. Neither should be taken seriously. This isn't Bradly Efron arguing with Andrew Gelman.

inimino 6y ago
Based on what I've read of Taleb, if you think he doesn't understand some patently obvious facts about probability, it's going to take more than saying that you watched a video and didn't think it made sense for me to give your claim any weight.
amw-zero 6y ago
There is a very clear flaw in your mathematical reasoning here, let's walk through it. Consider your second probability comparison: the difference between a probability of 0.500 and 0.501. You have this correct, the difference is 0.001. Now reconsider your first statement: that a probability of 0.010 is an order of magnitude more likely than a probability of 0.001. This is true, but is completely irrelevant because it is a completely different comparison. A more appropriate comparison would be to compare probabilities of 0.010 and 0.011. The difference of these is again 0.001. You compared proverbial apples to oranges, and you cannot trust the conclusions you make from invalid comparisons. A difference in probability of 0.001 does mean the same thing no matter what the starting probability is. Probability is "linear" in this way. Now that we know this to be true, I would encourage you to rethink your position on Nassim Taleb. He understands non-linearity quite well, in fact I would argue that his entire purpose on Earth (at least in his eyes) is to remind people about non-linearity as a concept. It comes across in all of his books and most of his public appearances. On the matter of probability, I trust him very deeply. Whether or not I trust him is also inconsequential, because he has serious mathematical literacy and you can evaluate his propositions for yourself.
- j7ake 6y ago
  The difference between probability 0.001 and 0 is also 0.001, but it's clearly not the same as a change in probability from 0.500 to 0.499. I think the point is that it's the change in the log-odds that make differences comparable, not the change in the linear scale.
  - amw-zero 6y ago
    The difference in those probabilities is the same. In each case, the event with the greater probability is 1-in-a-thousand times more likely to occur than the lesser. Let's walk through an example with these numbers. Each case has 2 probabilities and we'll assign them each to the possible outcomes of a coin flip. Case 1: The probability of heads is 0 and the probability of tails is 0.001. We flip the coin 1,000 times. The ideal outcome is that we see 0 heads and 1 tails. Case 2: The probability of heads is 0.499 and the probability of tails is 0.500. We flip the coin 1,000 times. The ideal outcome is that we see 499 heads and 500 tails. (You'll notice that the outcomes don't add up to 1,000 in either case, and that's because the probabilities don't add up to 1. That means there is actually a third possible outcome, but that can be ignored for the purpose of this example.) They each differ by a result of 1 result per 1,000 trials. This is because probability is simply the likelihood of an event occurring. There is no super-linear pattern going on here. It is no harder to get from 0.7 to 0.9 probability than it is to get from 0.2 to 0.4. It is just a measure of likelihood. What is causing people to misunderstand this? I wonder if you're thinking about probability distributions vs. probability itself?
    - j7ake 6y ago
      Adding and subtracting operations are natural in the log scale (think probability of multiple independent events), but not in the linear scale. The interpretation of a linear difference of 0.001 in probability depends on the two numbers you're subtracting, which is not the case in log scale. OP pointed out intuitively why adding and subtracting probabilities in the linear scale don't make sense (examples would be comparing 0.001 and 0 versus 0.500 and 0.499). It's the fold changes that matter when interpreting two different probabilities (e.g. making decisions under uncertainty), not the linear difference. The proper interpretation of your Case 1 and Case 2 should be the ratio of heads and tails as you flip coins, not the difference in the absolute number of heads that show up in the two cases.

inimino 6y ago

Based on what I've read of Taleb, if you think he doesn't understand some patently obvious facts about probability, it's going to take more than saying that you watched a video and didn't think it made sense for me to give your claim any weight.

amw-zero 6y ago

There is a very clear flaw in your mathematical reasoning here, let's walk through it. Consider your second probability comparison: the difference between a probability of 0.500 and 0.501. You have this correct, the difference is 0.001. Now reconsider your first statement: that a probability of 0.010 is an order of magnitude more likely than a probability of 0.001. This is true, but is completely irrelevant because it is a completely different comparison. A more appropriate comparison would be to compare probabilities of 0.010 and 0.011. The difference of these is again 0.001. You compared proverbial apples to oranges, and you cannot trust the conclusions you make from invalid comparisons. A difference in probability of 0.001 does mean the same thing no matter what the starting probability is. Probability is "linear" in this way. Now that we know this to be true, I would encourage you to rethink your position on Nassim Taleb. He understands non-linearity quite well, in fact I would argue that his entire purpose on Earth (at least in his eyes) is to remind people about non-linearity as a concept. It comes across in all of his books and most of his public appearances. On the matter of probability, I trust him very deeply. Whether or not I trust him is also inconsequential, because he has serious mathematical literacy and you can evaluate his propositions for yourself.

j7ake 6y ago
The difference between probability 0.001 and 0 is also 0.001, but it's clearly not the same as a change in probability from 0.500 to 0.499. I think the point is that it's the change in the log-odds that make differences comparable, not the change in the linear scale.
- amw-zero 6y ago
  The difference in those probabilities is the same. In each case, the event with the greater probability is 1-in-a-thousand times more likely to occur than the lesser. Let's walk through an example with these numbers. Each case has 2 probabilities and we'll assign them each to the possible outcomes of a coin flip. Case 1: The probability of heads is 0 and the probability of tails is 0.001. We flip the coin 1,000 times. The ideal outcome is that we see 0 heads and 1 tails. Case 2: The probability of heads is 0.499 and the probability of tails is 0.500. We flip the coin 1,000 times. The ideal outcome is that we see 499 heads and 500 tails. (You'll notice that the outcomes don't add up to 1,000 in either case, and that's because the probabilities don't add up to 1. That means there is actually a third possible outcome, but that can be ignored for the purpose of this example.) They each differ by a result of 1 result per 1,000 trials. This is because probability is simply the likelihood of an event occurring. There is no super-linear pattern going on here. It is no harder to get from 0.7 to 0.9 probability than it is to get from 0.2 to 0.4. It is just a measure of likelihood. What is causing people to misunderstand this? I wonder if you're thinking about probability distributions vs. probability itself?
  - j7ake 6y ago
    Adding and subtracting operations are natural in the log scale (think probability of multiple independent events), but not in the linear scale. The interpretation of a linear difference of 0.001 in probability depends on the two numbers you're subtracting, which is not the case in log scale. OP pointed out intuitively why adding and subtracting probabilities in the linear scale don't make sense (examples would be comparing 0.001 and 0 versus 0.500 and 0.499). It's the fold changes that matter when interpreting two different probabilities (e.g. making decisions under uncertainty), not the linear difference. The proper interpretation of your Case 1 and Case 2 should be the ratio of heads and tails as you flip coins, not the difference in the absolute number of heads that show up in the two cases.