Can you link to Nostalgebrist saying that his post was a math error at SSC? I can’t find it. Also, see Nostalgebrist’s update at the start of the critique:
To be clear, Bach’s use of a Gaussian is not the core problem here, it’s just a symptom of the core problem.
The core problem is that his curves do not come from a model of how disease is acquired, transmitted, etc. Instead they are a convenient functional form fitted to some parameters, with Bach making the call about which parameters should change – and how much – across different hypothetical scenarios.
Having a model is crucial when comparing one scenario to another, because it “keeps your accounting honest”: if you change one thing, everything causally downstream from that thing should also change.
Without a model, it’s possible to “forget” and not update a value after you change one of the inputs to that value.
That is what Bach does here: He assumes the number of total cases over the course of the epidemic will stay the same, whether or not we do what he calls “mild mitigation measures.” But the estimate he uses for this total – like most if not all such estimates out there – was computed directly from a specific value of the replication rate of the disease. Yet, all of the “mild mitigation measures” on the table right now would lower the replication rate of the disease – that’s what “slowing it down” means – and thus would lower the total.
Nowhere in that comment does he say that his post was or contained a “math error”. The closest thing I can find is this:
Great point about the step function. That convinces me that Bach would not have drawn a different qualitative conclusion if he had used a different functional form, no matter which one. I’ve updated my post with a note about this.
[EDIT: AFAICT Douglas_Knight is saying that Nostalgebrist’s initial guess that Bach’s post was sensitive to the functional form is a “math error”. I wouldn’t call it that, but perhaps reasonable people could disagree about this.]
What did his post originally mean? I’m not allowed to read people’s minds. He admits that no one took from it what he wanted them to take from it. Lanrian said that it was “a reasonable critique...that it doesn’t make sense to assume a normal distribution.” That was a qualitative complaint and he admitted that it was qualitatively wrong.
As I said, I do agree that the piece’s qualitative conclusion was correct. However, the gaussian assumption does make a large quantitative difference. Comparing it to the extreme: If we always have the maximum number of people in ICUs, continuously, the time until herd-immunity would be 4.9 years, which is a factor 3 less than what the normal assumption gives you. Although it is still clearly too much, it’s only one or two additional factors of 3 away from being reasonable. This extreme isn’t even that unrealistic; something like it could plausibly be achieved if the government continuously alternated between more or less lock-down, keeping the average R close to 1.
To be clear, I think that it’s good that the post was written, but I think it would have been substantially better if it had used a constant number of infected people. If you’re going to use unrealistic models (which, in many cases, you should!) it’s good practice to use the most conservative model possible, to ensure that your conclusion holds no matter what, and to let your reader see that it holds no matter what. In addition, it would have been simpler (you just have to multiply/divide 3 numbers), and it would have looked less like realistic-and-authoritative-math to the average reader, which would have better communicated its real epistemic status.
The gaussian assumption makes no difference. Nostalgebrist’s post is a math error. He later admitted that at SSC, but barely updated his post.
Can you link to Nostalgebrist saying that his post was a math error at SSC? I can’t find it. Also, see Nostalgebrist’s update at the start of the critique:
here
Nowhere in that comment does he say that his post was or contained a “math error”. The closest thing I can find is this:
[EDIT: AFAICT Douglas_Knight is saying that Nostalgebrist’s initial guess that Bach’s post was sensitive to the functional form is a “math error”. I wouldn’t call it that, but perhaps reasonable people could disagree about this.]
You’ve lost track of the object level here.
What did his post originally mean? I’m not allowed to read people’s minds. He admits that no one took from it what he wanted them to take from it. Lanrian said that it was “a reasonable critique...that it doesn’t make sense to assume a normal distribution.” That was a qualitative complaint and he admitted that it was qualitatively wrong.
As I said, I do agree that the piece’s qualitative conclusion was correct. However, the gaussian assumption does make a large quantitative difference. Comparing it to the extreme: If we always have the maximum number of people in ICUs, continuously, the time until herd-immunity would be 4.9 years, which is a factor 3 less than what the normal assumption gives you. Although it is still clearly too much, it’s only one or two additional factors of 3 away from being reasonable. This extreme isn’t even that unrealistic; something like it could plausibly be achieved if the government continuously alternated between more or less lock-down, keeping the average R close to 1.
To be clear, I think that it’s good that the post was written, but I think it would have been substantially better if it had used a constant number of infected people. If you’re going to use unrealistic models (which, in many cases, you should!) it’s good practice to use the most conservative model possible, to ensure that your conclusion holds no matter what, and to let your reader see that it holds no matter what. In addition, it would have been simpler (you just have to multiply/divide 3 numbers), and it would have looked less like realistic-and-authoritative-math to the average reader, which would have better communicated its real epistemic status.