They JUST released thr figures, its 373. I was bracing for a much bigger surge because of the tweet you linked. Thank lord its still under 400.
*Exhales*
They also shot above the 26k mark for tests. Keep it up.
I like to know what the venerable campfreddie thinks about today's numbers. They have had excellent posts about the figures from many of the affected countries.
The UK figures are good to see. Based on yesterday, about 425 cases would have been the exponential trend expectation. The trend over the last week is closer to a linear rise than an exponential.
It's way to early to be sure since we don't have enough data (e.g. Italy also showed a roughly linear trend 1-2 weeks ago, which gave me false hope at the time).
Optimistically, it could mean that people in the UK have adjusted their behaviour somewhat, and that his has moved us away from exponential conditons. Given the incubation/detection time, changes in behaviour take a few days to be reflected in the case numbers and it's been a week since it became obvious the virus was spreading here instead of being limited to people returning from holidays.
Doing confidence stats on the total cases is arguably a bit silly, since you're comparing to a null hypothesis of "the case number is not changing". That might be useful for convincing Donald Trump, but it's really weighting the odds in favour of finding something statistically different to the null hypothesis.
So, I also decided to plot the daily increase vs. time, instead of the total detected vs time. This is me getting
nerd-sniped.
The mathematical beauty of an exponential equation is that the curve shape gives zero fucks about calculus. By definition, an exponential function is one where the total number and rate of change (i.e. new cases per day) are both exponential, because the derivative of e^x = e^x.
The real world isn't so mathematically pure, so the rate of change data should be more sensitive than the total case numbers.
Graphs of total case numbers can "look" exponential just because the the rate of new cases increases over time, but it isn't truly exponential unless that rate of new cases is also exponentially increasing.
In Italy the daily new cases over time is also exponential. I can't be arsed to do a proper non-linear fit with stats programs, but a shitty spreadsheet's log fit gives me r-squared of 0.96 for rate of change vs time. That isn't proof of exponential growth, but it's a strong sign. A linear fit only gives R2 of 0.7, so we can be pretty sure that not only is the number of cases increasing (COVID is real), the number of new cases per day are increasing (paging Donald Trump), and that they're increasing by an ever-increasing rate (oh fuck). That's about as close as you'll get to proving an exponential growth is occurring.
Elsewhere In Europe though, the daily new cases plots are a mixed picture.
UK has an R-squared of 0.5 which is the statistical equivalent of that shrugging ASCII emoji thing. A linear fit also gives R-squared of 0.5, so you really can't say what's going on. The number of "cases per day" is going up by some value or other, I guess.
France and Germany are also pretty bad for exponential fits of daily new cases, with r-squared of 0.6 and 0.7.
I'm ignoring datapoints below 50 total cases since they'll be dominated by imported cases and not community spread. This means there's less data for the UK (only fitting 7 datapoints for the rate of change) and other countries (10 for France and Germany) so you'd expect less reliable fits. Just one datapoint can make a big difference, and COVID testing is far from an unbiased sample of the population.
If you're wondering how you can be both confident and also not confident of exponential growth, depending on which method you use to analyse the data, then welcome to the wonderful world of stats.
TL;DR - It's way too early to make conclusions about the UK case growth based on statistical analysis because the data are too messy and there aren't enough datapoints. Maybe we'll follow Italy's trend, but it's about equally possible (from a statistical point of view, not a mechanistic one) that we will not. Italy's case numbers could literally be used as a textbook example of exponential growth. Now wash your hands.
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