8 ms·

> A cubic polynomial vs time would be a terrible idea, but the dashed and/or dotted red line (that people seem upset about) is obviously not a cubic polynomial

> A cubic polynomial vs time would be a terrible idea, but the dashed and/or dotted red line (that people seem upset about) is obviously not a cubic polynomial vs time. What? The chart's creator said it was a cubic polynomial. Mr. Hassett said he had employed ‘just a canned function in Excel, a cubic polynomial.’” https://www.vox.com/2020/5/8/21250641/kevin-hassett-cubic-model-smoothing https://www.vox.com/2020/5/8/21250641/kevin-hassett-cubic-mo...

dnautics 6y ago
on the other hand, for reals calculus (namely taylor polynomial estimation) also says, "why not a cubic polynomial?"
- CrazyStat 6y ago
  Because Taylor approximations can lose accuracy very quickly as you move away from the point they are centered around. There are available epidemiological models that are actually grounded in a scientific understanding of the problem. "Why not a cubic polynomial?" is a stupid question.
  - mcnamaratw 6y ago
    "Why not a cubic polynomial?" taken literally is not a stupid question at all. No, it's not a contribution to understanding the problem at the professional level, but it is a fundamental and important question. Somebody persists after hearing the answer (which you gave), that might be stupid.
  - dnautics 6y ago
    Yes, and until you do the correct analysis and estimate just how bad the estimate is going to be (off by 10%? Off by 50%? An order of magnitude?) You can't just dismiss it out of hand. So how far off will it be?
    - CrazyStat 6y ago
      The cubic is going to go to either +infinity or -infinity, so it will eventually be of by infinity%. Or infinity orders of magnitude. I feel like I can dismiss it now.
      - dnautics 6y ago
        There's such thing as a convergence interval and your flippant comment betrays your ignorance.
        CrazyStat 6y ago
        Convergence interval doesn't help at all when you're working with a fixed finite polynomial (cubic, in this case). You don't need any flippancy to betray your ignorance, it's already clearly on display.
mcnamaratw 6y ago
Sorry to shock you, but not every piece of text on the internet holds water mathematically. Plot a cubic polynomial in time, at^3 + bt^2 + c*t + d. Use Excel. The curve either diverges to + or - infinity at each end, or it's a constant. That's not the behavior of the dashed red curve in the OP. What it could be is some kind of cubic spline. But it is not a cubic polynomial in time.
- rsfern 6y ago
  It’s apparently a cubic polynomial fit to the logged data — see http://bactra.org/weblog/1176.html http://bactra.org/weblog/1176.html
  - cousin_it 6y ago
    A cubic polynomial goes to +infinity on one side and -infinity on the other. So taking exp, log, etc won't make it go to 0 on both sides. I can think of two possible explanations: 1) the leading coefficient happens to be 0, so it's actually quadratic fit 2) the leading coefficient is nonzero, so somewhere to the left or right the graph starts rising again, but it's not visible due to cropping. Anyway by now we've spent more time thinking about this than any of the participants, so we should call it a day.

dnautics 6y ago

on the other hand, for reals calculus (namely taylor polynomial estimation) also says, "why not a cubic polynomial?"

CrazyStat 6y ago
Because Taylor approximations can lose accuracy very quickly as you move away from the point they are centered around. There are available epidemiological models that are actually grounded in a scientific understanding of the problem. "Why not a cubic polynomial?" is a stupid question.
- mcnamaratw 6y ago
  "Why not a cubic polynomial?" taken literally is not a stupid question at all. No, it's not a contribution to understanding the problem at the professional level, but it is a fundamental and important question. Somebody persists after hearing the answer (which you gave), that might be stupid.
- dnautics 6y ago
  Yes, and until you do the correct analysis and estimate just how bad the estimate is going to be (off by 10%? Off by 50%? An order of magnitude?) You can't just dismiss it out of hand. So how far off will it be?
  - CrazyStat 6y ago
    The cubic is going to go to either +infinity or -infinity, so it will eventually be of by infinity%. Or infinity orders of magnitude. I feel like I can dismiss it now.
    - dnautics 6y ago
      There's such thing as a convergence interval and your flippant comment betrays your ignorance.
      - CrazyStat 6y ago
        Convergence interval doesn't help at all when you're working with a fixed finite polynomial (cubic, in this case). You don't need any flippancy to betray your ignorance, it's already clearly on display.

mcnamaratw 6y ago

Sorry to shock you, but not every piece of text on the internet holds water mathematically. Plot a cubic polynomial in time, at^3 + bt^2 + c*t + d. Use Excel. The curve either diverges to + or - infinity at each end, or it's a constant. That's not the behavior of the dashed red curve in the OP. What it could be is some kind of cubic spline. But it is not a cubic polynomial in time.

rsfern 6y ago
It’s apparently a cubic polynomial fit to the logged data — see http://bactra.org/weblog/1176.html http://bactra.org/weblog/1176.html
- cousin_it 6y ago
  A cubic polynomial goes to +infinity on one side and -infinity on the other. So taking exp, log, etc won't make it go to 0 on both sides. I can think of two possible explanations: 1) the leading coefficient happens to be 0, so it's actually quadratic fit 2) the leading coefficient is nonzero, so somewhere to the left or right the graph starts rising again, but it's not visible due to cropping. Anyway by now we've spent more time thinking about this than any of the participants, so we should call it a day.