Pretty sure we decided that they fit a cubic to log(deaths), not to deaths. So log(deaths) goes to negative infinity as deaths goes to zero.
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Replying to @ProfJayDaigle
This is what I get when I fit a cubic to log(deaths) and then exponentiate so I can match the original linear scale plot. You're the math expert, but the coefficient of x^3 is > 0 so this should go to infinity, right?pic.twitter.com/6yKhw80Mvt
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Replying to @danluu @ProfJayDaigle
To be fair (?) to the authors of the original graph, if we fit against data as of May 5th, then deaths goes to negative infinity. If taken seriously, this would indicate a pretty serious failure of "flattening the curve".
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Replying to @danluu
Exactly. (I was trying to double-check that that was the case before you confirmed it for me.) One reason that a cubic model is dumb is that it's _incredibly_ sensitive to adding or changing a few points. A cubic model will _magnify_ small variations in recent data.
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Replying to @ProfJayDaigle @danluu
But what they did on May 5 was fit a cubic to log(deaths), see that it went to negative infinity, and thus projected log(deaths) would go to negative infinity and thus deaths would go to zero.
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Replying to @ProfJayDaigle @danluu
Cubics can be good for smoothing or interpolating a complete data series. But they're awful for projecting beyond the end of a data series, because they're _gonna_ go to +/- infinity and which one they pick is nearly random in the absence of a clear trend through the last points.
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Replying to @ProfJayDaigle
This is a pet peeve of mine! Just for example, in old software engineering papers (the kinds of things published in FSE or ICSE), you can find spectacularly inappropriate quadratic or cubic fits used to support a conclusion that's unsupported by the data.
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Replying to @danluu @ProfJayDaigle
Dan Luu Retweeted quarentanja
Also, I'm annoyed that I wrote deaths and not log(deaths) in the original tweet and there's no good way to amend this without deleting the entire set of tweets and re-writing them (which I might do, IDK), perhttps://twitter.com/anjakefala/status/1254479204810403841 …
Dan Luu added,
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I'm actually envious of communities that carry out discussions on FB instead of Twitter since the tools FB provides are so much better. I think it's a pretty bad sign when you long for a Facebook level of support for nuanced discussions, but here we are.
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