Timeline for A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so from the statistics viewpoint?
Current License: CC BY-SA 4.0
20 events
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| May 23, 2020 at 18:16 | vote | accept | CopperKettle | ||
| May 22, 2020 at 16:34 | comment | added | Wrzlprmft | @whuber: I asked a follow-up question on this. | |
| May 22, 2020 at 13:51 | comment | added | whuber♦ | @Wrzlprmft Yes, it is honest-to-God bootstrapping. There are various flavors. This one is parametric in the sense of assuming the data arise as independent realizations of Poisson variables--in effect, an inhomogeneous Poisson process. There is no "null model" or other hypothesis in effect. | |
| May 22, 2020 at 13:26 | comment | added | Wrzlprmft | Is this really what is usually called bootstrapping? I would call this a Monte Carlo sampling of a null model, surrogate, or similar. (Mind that this just about terminology; the analysis seems completely sound to me.) | |
| May 22, 2020 at 1:25 | comment | added | Aksakal | @SextusEmpiricus I scraped the plot that’s in my answer, and the url is there too. | |
| May 22, 2020 at 1:23 | comment | added | Sextus Empiricus | @Aksakal a plausible explanation could be that all positive cases found in a local lab are being re-tested in a national lab, and the numbers from that lab are being reported. Maybe you could do your answer for the case of Московская область (how did you get the data for the city only?) which has ~1000 cases/day with low dispersion. I would not be surprised if again you find higher dispersion in the sub-regions. | |
| May 22, 2020 at 0:59 | comment | added | Aksakal | @SextusEmpiricus it could be anything like this regions doesn’t want to be worse than the next region so they lookup the average and cap their report | |
| May 22, 2020 at 0:58 | comment | added | Sextus Empiricus | @Aksakal I realize by now that the numbers are indeed counts, although I have still doubts what sort of counting process generated it (it is only an assumption that these counts are counts from a Poisson process). Maybe it is some batch process, where the cases are reported per 100. Or maybe it is something else. In order to know whether these numbers are suspicious we should not run our models and computations, but instead dig up information about the process that generated the data. | |
| May 22, 2020 at 0:55 | comment | added | Aksakal | @SextusEmpiricus the numbers are counts | |
| S May 21, 2020 at 19:02 | history | suggested | CommunityBot | CC BY-SA 4.0 |
Fixed a typo
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| May 21, 2020 at 18:59 | review | Suggested edits | |||
| S May 21, 2020 at 19:02 | |||||
| May 21, 2020 at 15:33 | comment | added | whuber♦ | @Sextus I have no idea what you mean by "gaps" and "weekends suddenly gone:" they are present in the graphic in the question and there are no visible gaps. The p-value will be much lower than 1/2001 simply by running more bootstrap iterations. Try it! (I just reran the code with $k=d=6$ for 20,000 iterations and now the p-value is at 1/20001, which is as small as it can possibly be for this number of iterations.) | |
| May 21, 2020 at 14:55 | comment | added | whuber♦ |
@COOL As I explained, there's nothing special about the model. What makes this analysis work is that when we vary the number of knots and degree of the splines, to adjust the degree of overfitting, the result stays the same. I have explored ranges of 2 through 12 for k and 3 through 6 for d. We could do the same by employing lowess models with varying degrees of tension as well as by many other regression models.
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| May 21, 2020 at 14:51 | comment | added | COOLSerdash | What's the reason you opted for splines with degree 4? I re-run your code with cubic splines and the fit was indeed much worse. | |
| May 21, 2020 at 14:32 | comment | added | whuber♦ | BTW, my initial reaction was to focus on weekends because they exhibit no dips at all: that's an extraordinary departure from the reporting habits of many other countries. But, not wishing to speculate about such issues, and wishing not to become embroiled in finer details of time series analysis, I opted for the simpler exploratory approach I have outlined here. | |
| May 21, 2020 at 14:30 | comment | added | whuber♦ |
@Sextus That's an interesting observation. I am indeed suspicious that the numbers might not be counts. But they're definitely not cases per thousand--that would sum to more cases than people! In any region in Russia, the total of a few thousand looks like it's the right order of magnitude. For these data to survive my analysis, they would have to represent counts at least three times larger than the raw numbers. (I worked this out simply by multiplying y by 3 in the code and re-running it, then doing that again with a multiple of 10.)
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| May 21, 2020 at 14:24 | comment | added | Sextus Empiricus | You assume a Poisson distribution but are we really looking at counts from a Poisson process? Maybe the numbers are 'per thousand' and not counts or maybe they are a percentage or scaled such that a maximum equals hundred (like Google trend data)? Maybe the numbers are not from a Poisson process, and they relate to some limit of the process (e.g. lots of these data have gaps in the weekends when less data is processed)? The conclusion that these data are 'out of the extraordinary' depends on these assumptions. | |
| May 21, 2020 at 13:30 | history | edited | whuber♦ | CC BY-SA 4.0 |
Corrected "5000" to "2000" to agree with the code and figures.
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| May 21, 2020 at 13:25 | comment | added | EngrStudent | Your answers are always exceptional. I love reading them because I love learning, and I learn a lot from you. Thank you. | |
| May 21, 2020 at 13:22 | history | answered | whuber♦ | CC BY-SA 4.0 |