Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Show HN: Log-Scale Covid-19 Plots

bitbucket.org

Post reply on HN
Print view View original

71–75 of 75 posts

Re: Show HN: Log-Scale Covid-19 Plots

#71

Post by dragonwriter »

m0zg wrote: post #68
dragonwriter wrote: post #39

Earlier quoted context omitted.

> All of these need to be normalized per capita. Otherwise you don't see the true extent of the problem. Normalizing per capita replaces the true extent of the problem with the true relative local impact of the problem; both are significant.

But relative local impact _is_ the extent. If you live in a village of 100 people and 10 die that's pretty bad. If you live in NYC and 10 die - that's statistical noise that nobody will even notice.

> But relative local impact _is_ the extent.

No, absolute scale is the extent, that's pretty much what “extent” means.

Relative local impact is the...well, relative local impact.

Both are important, though which is more important depends on what you are doing with the measure.

Re: Show HN: Log-Scale Covid-19 Plots

#72

Post by FabHK »

dhimes wrote: post #67
FabHK wrote: post #59

Earlier quoted context omitted.

The turning point is when the second derivative is zero, which would indeed be easy to spot with a second derivative graph. But it’s also very easy to spot with the first derivative graph (as published by the FT now): It’s when the first derivative hits its maximum.

Yes- but I'm talking about the inflection point- where the curve goes from concave up to concave down. These are modeled as gaussians- so if that modeling works we would be a standard deviation from the peak- assuming the crisis is being well managed.

By turning point I mean the inflection point. You turn from “driving left” (convex) to “driving right” (concave).

By the way, the derivative of the logistic function is the logistic distribution, and that’s not the Gaussian bell shape, it has much fatter tails: Gaussian tails drop much faster, with exp(-x^2), while the logistic drops with exp(-|x|). (Makes sense, as the logistic curve grows exponentially at the beginning, and the derivative of the exponential is the exponential.)

Re: Show HN: Log-Scale Covid-19 Plots

#73

Post by dhimes »

FabHK wrote: post #72
dhimes wrote: post #67

Earlier quoted context omitted.

Yes- but I'm talking about the inflection point- where the curve goes from concave up to concave down. These are modeled as gaussians- so if that modeling works we would be a standard deviation from the peak- assuming the crisis is being well managed.

By turning point I mean the inflection point. You turn from “driving left” (convex) to “driving right” (concave). By the way, the derivative of the logistic function is the logistic distribution, and that’s not the Gaussian bell shape, it has much fatter tails: Gaussian tails drop much faster, with exp(-x^2), while the logistic drops with exp(-|x|). (Makes sense, as the logistic curve grows exponentially at the begin…

haha yes indeed. I had never heard the term "turning point" used like that, but I guess it makes sense if you think about it as the turning point of the first derivative.

But I learned what a logistic function is, so thank you. I guess that is needed for the cumulative count.

You might be interested in this. I posted it a few days ago- it's why I'm talking Gaussians.

https://www.medrxiv.org/content/10.1101/2020.03.27.20043752v...

Re: Show HN: Log-Scale Covid-19 Plots

#74

Post by lopmotr »

LaszloKv wrote: post #52
adventured wrote: post #46

Earlier quoted context omitted.

It also needs per capita figures, which is dramatically more important than absolute figures, unless everyone happens to know the population figures of each country by memory. You end up missing critical data points like the per 100k population mortality rates (from Friday morning): New York 12, Louisiana 6.6, New Jersey 6, Michigan 4.2, Washington 3.5, Connecticut 3.1, Massachusetts 2.2, Colorado 1.7, Georgia 1.67,…

In this video John Burn-Murdoch (the creator of the FT charts) discusses why they decided against showing numbers per capita. https://mobile.twitter.com/janinegibson/status/1244519429825... There's also this tweet additionally showing how population size of a country has no relationship to pace of disease spread. https://mobile.twitter.com/jburnmurdoch/status/1246185741304...

There's another surprising reason why per capita numbers aren't useful - for exponential growth on the typical type of graph starting at some "initial" number of cases, it makes no difference! For example, if one country was counted a two equal half-sized countries, their graphs would be the same shape but shifted to the right by a few days. However, they would also reach their "initial" number of cases where the graphs start at a few days later - shifting them left by the same amount! The result would be the same line as the full-sized country.

Re: Show HN: Log-Scale Covid-19 Plots

#75

Post by lopmotr »

noctilux wrote: post #5
jaakl wrote: post #4

Earlier quoted context omitted.

I tried, it does not work that way if you think. Or at least your “population” spec should be not arbitrary current administrative region or country, but specific virus spread area, which is very difficult to get data. You’ll get weird absolute numbers for EU minicountries (San Marino and Luxembourg are top) and very different figures per China, Hubei and other regions there. And if you finally compare in graphs you’…

Agree. I was confused by this at first but if the slope on lines without dividing by population is: (log y2 - log y1) / (x2 - x1) Then if we scale y2 and y1 both by c, which is 1 / population: (log( c * y2 ) - log( c * y1 )) / (x2 - x1) = (log c + log y2 - log c - log y1) / (x2 - x1) = (log y2 - log y1) / (x2 - x1) So scaling by population does not change the slope of the graphs, only the intercept.

It doesn't even change the intercept because bigger countries reach their threshold number of cases sooner so that shifts them back again. Hence most of the lines are all roughly on top of each other regardless of country size.
Post reply on HN