Information Matrix

It is well-known that Isaac Newton invented the calculus, and that his laws of motion and gravitation launched mathematical physics. Some brilliant British physicists carried on the tradition; think of Hamilton, Maxwell, Kelvin* et al. But where were the mathematicians? The answer is: across the English Channel.

Binary oppositions come easily to the human mind. Good and evil. Joy and sadness. Chalk and cheese. But, attracted as we are to neat categories, one question is whether these clean absolutes always exist in reality?

Today is the 200th anniversary of Benjamin Gompertz's reading of his famous paper before the Royal Society of London.  Generations of actuaries and demographers are familiar with his law of mortality:

\[\mu_x = e^{\alpha+\beta x}\qquad(1),\]

I rediscovered my Faculty of Actuaries diploma recently, having misplaced it in a house move some years ago. It testifies to my knowledge of ‘the doctrine of probabilities’, which is nice. But not long after I received it, Prof Hans Bühlmann classified actuaries like me as ‘Actuaries of the First Kind’ and said:

Contrary to [the Actuary] of the First Kind in life assurance, whose methods were essentially deterministic, [the Actuary of the Second Kind] had to master the skills of probabilistic thinking.

We last reported on Chimeric Antigen Receptor (CAR) T-cell immunotherapy treatments in a blog from 2018, where it was noted that progress within solid tumour cancers was still at early stages.

In my previous blog I described a real case where so-called artificial intelligence (AI) would have struggled to spot data problems that a (suspicious) human could find.  But what if the input data are clean and reliable?

Stephen and our late and much-missed colleague Iain Currie each once marked the presentation of a paper to a sessional meeting of the IFoA by penning some verse for the dinner that followed.  The recent presentation of Macdonald & Richards (2024) therefore provided my excuse for the following lines.

Regular readers of this blog (both of them) will have noticed how often we advocate that actuaries use the Kaplan-Meier estimator in their mortality analysis.  While parametric survival models are best for multi-factor models, the Kaplan-Meier estimate is exceptionally useful for visualisation, communication and data-quality checking.

Stephen recently questioned whether the hype around AI models for Life Insurance might be a case of The Emperor's New Clothes. In this blog we discuss an important point of difference: whereas in the fable, a youth reveals the expensive "invisible" new clothes have no substance at all, in our scenario, we find precisely the opposite. AI models utilising machine learning are, far from being see-through, simply not transparent enough.

Look in any good bookshop (or on Amazon) and you will find any number of books describing the spectacular failures of financial institutions.