@JimB Comparison point, Exp[a x^2 + b x + c] over the "smooth" range of Chinese data:

With[{data = {4515, 5974, 7717, 9692, 11948, 14380, 17205, 20440,
     24324, 28018, 31161, 34546, 37198, 40171, 42638, 44653, 46472,
     48467}},
  NonlinearModelFit[data,
   Exp[a x^2 + b x + c], {{a, 0}, {b, 0.3}, {c, 8}}, x,
   Weights -> 1/data]]["RSquared"]

(* 0.99982 *)

And if you ignore the last point of that data, it's over 0.9999.

@kirma A high R^2 with available data does not mean that extrapolation is automatically warranted. I also assume that much of the smoothness comes from the cumulative total counts. And the use of cumulative counts certainly deviates from the assumption of independence of observations that the regression approach assumes.

The plot of the differences does not have a plausible/believable/natural shape: ListPlot[Differences[data]].

Guys if you are interested in the COVID-19 history data of china, here is a nice data source: github.com/BlankerL/DXY-COVID-19-Crawler/blob/master/…

Note it's not by me. I only found it just now. It covers data down to every cities in every provinces. The data source itself comes from Ding Xiang Yuan, as I know is an online non-gov society of doctors and nurses from mainland china.

@JimB I'm just saying that especially that section of official data follows such a neat curve that I'd think even officials would have had troubles thinking that it wouldn't cause significant questioning.

Can anybody help this user out? mathematica.stackexchange.com/questions/215235/…

Nevermind 😂

Gif export is so slow as to be virtually pointless within WL.

and then it exports and you remember that you didn't add AnimationRepititions->Infinity

@kirma Got it. Another aspect to check out is the amount of variability about the curve. Because these are counts, it might be expected that the variance for each day might be at least as large as the variability of a Poisson random variable (hence your use of weight with variance proportional to the mean). But in this case that doesn't appear to be an issue.

Here's an animated figure with showing a sequence of 100 samples assuming the estimated curve is the true curve with the "Poisson variation" displayed.

Now in real life one would probably expect more than "Poisson variation" but in this case there appears to be at least Poisson variation. (Mathematica has yet to implement generalized linear MIXED models that allow for more than one source of variation. Although I know it's not easy to implement. If you think that folks have issues with lack of convergence from other methods now, just wait for mixed models to appear on the scene.)

@JimB Hmm, interesting.

@CarlLange It's brutal. Maybe the new video stuff they're adding will allow it to work somewhat better since it won't be basically rasterizing 100s of images and slowly, painstakingly stitching them into a GIF.

Wow! Lots of new features coming to 12.1. I think my favorite is childishly the ToonShading

@JimB Do you use R for stats instead?

@ChrisK. R and SAS for mixed models. R and Mathematica for graphics.