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Collated mortality insights

These are the collated mortality insights from all my blog articles.

Insight 1. Always allow for overdispersion

If you don’t allow for overdispersion then you will underestimate uncertainty and overfit models.

[Original article]

Insight 2. Experience data is ‘measurable‘

Provided we use measures, we’ll always get the same answer regardless of how an experience dataset is partitioned.

In particular, there is no need

  • for experience time periods to be contiguous1 – the sole requirement is that elements of the experience datasets do not intersect, or
  • to track individuals across experience datasets relating to different time periods2.

[Original article]

Insight 3. The continuous time definitions of A and E are canonical

The continuous time definitions of \(A\) and \(E\) are measures and the canonical definitions of actual and expected deaths.

Other definitions can lead to confusion – usually over \(\text{E}\) vs true expectation – and spurious complexity.

[Original article]

Insight 4. The expected value of A−E is zero

If \(\mu\) is the true mortality then the expected value of \(\text{A}f-\text{E}f\) is zero

  • for any variable \(f\) (even if \(f\) was used to fit the mortality in question), and
  • for any subset of the experience data (provided the choice of subset does not depend on E2R information).

[Original article]

Insight 5. The same machinery that defines A−E can be used to estimate its uncertainty

If \(\mu\) is the true mortality then the variance of \(\text{A}f-\text{E}f\) equals the expected value of \(\text{E}f^2\).

(This is before allowing for overdispersion.)

[Original article]

Insight 6. A/E variance increases with concentration

\(\sqrt{\text{E}w^2} / \text{E}w\), where \(w\ge0\) is a useful and recurring measure of effective concentration in relation to mortality uncertainty. It implies that the more concentrated the experience data (in some sense) then the greater the variance of observed mortality.

Using unweighted variance without adjustment to estimate weighted statistics will likely understate risk.

[Original article]

  1. An obvious example is excluding mortality experience from the height of the COVID-19 pandemic, potentially resulting in non-contiguous data from before and after the excluded time period. ↩

  2. Tracking individuals across experience datasets for different time periods may however be a very sensible data check. ↩