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
This is why I'm a big believer, philosophically, in fundamentals-based models rather than curve-fitting. A quadratic is a good model _if_ you have reason to believe that your data should fit a quadratic well!
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Replying to @ProfJayDaigle @danluu
You can also improve things with cross-validation; if the May 5 cubic model still looked good when fit against the May 15 data, that would be evidence in its favor. But without either a fundamentals model or good cross-validation, your fitted curve is probably bullshit.
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Replying to @ProfJayDaigle
Yeah, I started studying stats a bit in my spare time since I keep running into data related problems. Before I started, I thought I might be able to turn a lot of the thinking I do into mechanical processes, but I don't think that's really been the case at all.
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Dan Luu Retweeted Dan Luu
Andrew Gelman, Statistical Rethinking, etc., all emphasize how these techniques aren't substitutes for deeply understanding the problem domain. I agree there are techniques that are helpful checks, but applying them blindly can really go off the railshttps://twitter.com/danluu/status/1162139780299145216?lang=en …
Dan Luu added,
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Replying to @danluu @ProfJayDaigle
I can't tell if this is really different from programming or not? My feeling is that programming is easier to do mechanically (when you're not inventing truly novel algorithms or whatever), but I don't think I can really justify that feeling.
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Replying to @danluu
My impression as an outsider is that the day-to-day of data science includes a fair amount of mechanical bits and also a fair amount of judgment. But surely lots of programming is the same, where you need to figure out what the user _actually_ wants from what they say they want.
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