Page 22 of 22
Re: Are there .5% or 35 million Active Killers at Present?
Posted: Sat Jul 10, 2021 10:10 am
by Skepdick
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.
To avoid this level of nit-picking I am talking about the probability density function of human age. I am talking about THAT mean.
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.
Re: Are there .5% or 35 million Active Killers at Present?
Posted: Mon Jul 12, 2021 6:36 am
by jayjacobus
Skepdick wrote: ↑Sat Jul 10, 2021 10:10 am
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.
To avoid this level of nit-picking I am talking about the probability density function of human age. I am talking about THAT mean.
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.
What do you mean by "exact time-interval"?
Also, you can interpolate recklessly but you better not extrapolate recklessly.
Re: Are there .5% or 35 million Active Killers at Present?
Posted: Mon Jul 12, 2021 7:56 am
by Skepdick
jayjacobus wrote: ↑Mon Jul 12, 2021 6:36 am
What do you mean by "exact time-interval"?
I mean "at the time-interval where the discontinuity is being observed".
jayjacobus wrote: ↑Mon Jul 12, 2021 6:36 am
Also, you can interpolate recklessly but you better not extrapolate recklessly.
Do you think the extrapolation that human longevity is likely to trend upwards is "reckless"? Why?
Re: Are there .5% or 35 million Active Killers at Present?
Posted: Mon Jul 12, 2021 3:40 pm
by jayjacobus
Skepdick wrote: ↑Mon Jul 12, 2021 7:56 am
jayjacobus wrote: ↑Mon Jul 12, 2021 6:36 am
What do you mean by "exact time-interval"?
I mean "at the time-interval where the discontinuity is being observed".
jayjacobus wrote: ↑Mon Jul 12, 2021 6:36 am
Also, you can interpolate recklessly but you better not extrapolate recklessly.
Do you think the extrapolation that human longevity is likely to trend upwards is "reckless"? Why?
I don't know. I know that extrapolation can be done with a linear trend line, regression analysis, fitting a polynomial equation, making an intuitive interpretation of the data, using an average or median and/or modeling.
"The Actuary and IBNR," was co-authored by Ron Bornhuetter and Ron Ferguson. Like other loss reserving techniques, the Bornhuetter–Ferguson method aims to estimate incurred but not reported insurance claim amounts but applies to any estimating of future occurrences.