To avoid this level of nit-picking I am talking about the probability density function of human age. I am talking about THAT mean.jayjacobus wrote: ↑Wed Jul 07, 2021 4:08 am Be careful when trending data. There are often discontinuities in the data.
If the data points are 1203, 1196, 1374, 1282, 1596, 1638, 1745 and 1400, then you cannot fit a line to the data because there is a discontinuity and the fitted line will not explain the discontinuity. The average of the first 4 numbers is 1263.75 and the average of the last 4 numbers is 1594.75. The difference is 331. You can add 331 to each of the first 4 numbers to adjust for the discontinuity.
Is that the right thing to do? Only if you know what caused the discontinuity, can you be sure.
In the data for Covid 19 there are huge discontinuities. The analysts must understand the reasons for these discontinuities. If they don’t, their projections are reckless.
For longevity, the past trend is not linear and you cannot use a linear trend. The average life expectancy in 2221 will probably not be 115 on average.
The mathematical reason why discontinuities in the PDF are a "problem" is because you can't integrate a discontinuous function. Obviously! But you can interpolate a discontinuous function.
So if you are warning about the danger of interpolation, sure..... but interpolation is only a problem IF:
A. There is a discontinuity
B. There is a statistically significant deviation from norm at that exact time-interval.
Both of those things happening at the same time is less likely than any one of them happening individually. P(A+B) < P(A) || P(B)
So, once we interpolate the missing data it really is a a yes/no question: Is human life expectancy increasing as time progresses? And the answer is "Yes!" (within very high confidence)
If you still think this approach is "reckless", then I think your approach is no better than flipping a coin.