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“Just to give you an idea of how bad that is, a three-sigma or a one-in-200-year catastrophe would be 10% increase over pre-pandemic,” he said. “So 40% is just unheard of.”

This sounds very strange indeed, I'd like to see the numbers. For instance Euromomo https://www.euromomo.eu collects the statistics about death rates, here is a plot for the Italian death rate and you can see the mortality spikes with the covid waves, but those are quite specific for the elderly https://imgur.com/a/8cUdNcb

It sounds very strange that the death spike is "over" 3 sigma, which should mean over 3 standard deviations, which is really unbelievable, to me this looks like an artefact of some sort

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> It sounds very strange that the death spike is "over" 3 sigma, which should mean over 3 standard deviations, which is really unbelievable, to me this looks like an artefact of some sort

Why does the fact that it is larger than 3 standard deviations suggest to you that it must be an artifact? If the death rate is normally very stable then the standard deviation will be small, so it will be easy for any unusual increase to exceed that.

I think the other thing that may be possible (just guessing, I'm not a statistician or actuarial) is that by using the term "3 sigma" I'm assuming they're modeling the data as a normal distribution. But these types of outlier events often follow power laws, such that you get "fat tails" when looking at a bell curve.

> that by using the term "3 sigma" I'm assuming they're modeling the data as a normal distribution

variance and standard deviation don't only apply to normal distributions. and "sigma" is the symbol normally used for variance regardless of the underlying distribution.

> I'm assuming

sigh.

Yes, I'm fully aware that variance and standard deviation apply to any sample or population, and that sigma is normally used for standard deviation.

However, in everyday usage, saying something is a "2 or 3 sigma" event nearly always refers to a normal distribution unless otherwise noted, because otherwise that information doesn't really tell you anything. Is only with a specific distribution that can imply a percentage likelihood, e.g. 5% for a 2 sigma event or .3% for a 3 sigma event. Also, if you're looking at at annual probability, 1-in-200 year event would correspond to just about 3 sigma on a normal distribution.

Sigh

And the number of people dying per (large) unit of time is almost certainly well approximated by a normal distribution, modulo seasonal variation and events such as this (which break the "independence" assumption of the CLT).

The point is that you expect a normal distribution without fat tails. Fat tails are a sign of non random processes. Which lets you know some non random process is happening.

As the sibling comment wrote, it's not non-random processes in this instance, it's processes that aren't independent.

That is, when generally looking over any death rates in a relatively large population, most deaths in a given year are uncorrelated, so things look like a normal distribution. Obviously with a transmissible virus, the fact that two people died in the same year of Covid is correlated.

Similarly, if you did the math from the insurance company's data, I'd bet you'd find the chance of everybody dying in the same year would be like 1 in many, many trillions of years. But of course things like supervolcanos or meteor strikes are possible. Those aren't non-random, it's just that everyone's death would correlate with that single event.

Doesn't seem that is unbelievable at all to me. Instead I think it just highlights how humans can discount the severity of something when it moves slowly and continues for years.

Remember the Boxing Day tsunami in 2004 that was a major catastrophe around the world? According to a Google search it killed 227,898 people. Last I checked Covid had killed about 5.5 million, which is worse that every single war since WWII.

Of course, I think it's very fair to say the devastation from a war is much worse than Covid (a war destroys infrastructure and primarily kills the young), but from a pure "number of deaths" perspective I think most people have a huge difficulty comprehending the severity of the pandemic.

You probably should use this measure instead: https://en.wikipedia.org/wiki/Life-years_lost

Regardless of what measure you’re using it would also be good to make it per person.

Covid has obviously caused infrastructure problems, though the contrast with a war is similar. There are tons of minor maintenance tasks where there are one or two people who need to do some thing every week. Maybe all the people who are responsible for the task are laid up for a week and incapable of doing the maintenance. Multiply that by hundreds of thousands of people getting infected every week you end up with a lot of missed maintenance. And of course the risk that those one or two or three key people die and the task never gets done again until the system just hits the failure mode that the task was intended to avoid.

It was definitely a rickety system before Covid impacted it. But I suspect any strong shock could have caused a similar destabilization.

> but from a pure "number of deaths" perspective I think most people have a huge difficulty comprehending the severity of the pandemic.

Some 55 million people die each year. An extra 5 million is a big deal, yes, but there's almost 8 billion people on the planet. I think most people have a huge difficulty comprehending just how many humans there are on earth.

"see the numbers?" This story is from a life insurance company. It doesn't say "the death rate is up overall". It says "our policyholders are dying at an astonishingly high rate."

And it is indeed a very high rate.

The insurance guy was civilized enough not to complain that his company's incurring lots of losses -- getting hammered by writing lots of checks to survivors. But surely that's how an insurance company knows what's going on.

It makes no sense for an executive of a mutual insurance company to sling bs about this kind of loss. Because auditors.

> It sounds very strange that the death spike is "over" 3 sigma, which should mean over 3 standard deviations, which is really unbelievable, to me this looks like an artefact of some sort

It's not an artifact, it's incorrect modeling. If they're talking about sigmas, then they're modeling deaths as being normally distributed. But deaths aren't normally distributed, as you can tell by glancing at a graph of deaths over time: there's way more probability mass in the extremes than you would expect from a normal distribution. This sort of thing (modelling something poorly, then getting all surprised when reality violates your model) is depressingly common.

https://www.macrotrends.net/countries/USA/united-states/deat...

Overall death rates are highly affected by age distribution in the population - the proportion of 80-100 year olds in your population in a given year is going to have a big impact on the death rate that year.

Death rates for an age range (like 18-45) are likely to be much more stable.

Also, pretty dubious about that specific dataset - it looks like it includes linear interpolations between a much smaller set of actual datapoints, so not sure you can use it to infer the actual distribution of death rate statistics

> Death rates for an age range (like 18-45) are likely to be much more stable.

Do you have a data set for this to look at? I'm skeptical that death rates of any kind are close to normally distributed. If nothing else, there are big spikes during plagues, like the black plague and spanish flu.

You can't assume a standard normal distribution for something like death rates that are know to have a very high prevalence of right tail events like famine, war, and disease.

Isn't sigma for normal distributions of data? Is death rate normal on a 200-year timescale?

If the dataset which went into the «3 sigma» had no major catastrophes, like WW2 / covid / … then such an event can probably get you into «3 sigma territory».

> 3 standard deviations, which is really unbelievable

People reporting on deaths have to average over a period, otherwise you find deaths drop on weekends and spike on mondays because that's when the paperwork gets processed. In this case, they're averaging over an entire quarter.

I could well believe that the variance in death rates between Q4 2008 and Q4 2018 had a standard deviation of 3% - an entire quarter is a lot of averaging.

If you did it annually, you'd get rid of seasonal effects and probably get a smaller std dev. Using quarters gives you the full variability of the seasons, so it is a more conservative 3 sigma, in a sense.

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