In a recent blog, I looked at the most fundamental unit of observation in a mortality study, namely an individual life.  But is there such a thing as a fundamental unit of modelling mortality?  In Macdonald & Richards (2024) we argue that there is, namely an infinitesimal Bernoulli trial based on the mortality hazard.

In Macdonald & Richards (2024), Angus and I continue our long-standing advocacy for using individual records for mortality analysis, rather than grouped counts of lives.  One argument in our paper is that the individual life is the most irreducible unit of observation in mortality analysis.  After all, any group can be disaggregated into individuals, but further subdivision would just be dismemberment.

In a (much) earlier blog, Angus introduced the product-integral representation of the survival function:

\[{}_tp_x = \prod_0^t(1-\mu_{x+s}ds),\qquad(1)\]

A common approach to teaching students about mortality is to view survival as a Bernoulli trial over one year. This view proposes that, if a life alive now is aged \(x\), whether the life dies in the coming year is a Bernoulli trial with the probability of death equal to \(q_x\).  With enough observations, one can estimate \(\hat q_x\), which is the basis of the life tables historically used by actuaries.

On 29th August 2024 Professor Angus S. Macdonald and Dr. Stephen J. Richards will give a joint seminar on contemporary mortality modelling, in principle and in practice.  Attendance is free and pre-registration is not required.

The seminar will take place at 11:45hrs in Room T.01 in the Colin Maclaurin building at Heriot-Watt's Riccarton campus.  See also the campus map for location and parking.

The Institute and Faculty of Actuaries (IFoA) is hosting a meeting on contemporary mortality modelling on 24th October 2024.  Booking details can be found on the IFoA website.

Longevitas is pleased to announce that the Government Actuary’s Department has licensed the Longevitas survival-modelling software.  Further details can be found in the press release.

Actuaries denote with \({}_tp_x\) the probability that a life alive aged exactly \(x\) years will survive a further \(t\) years or more.  The most basic result in survival analysis is the following relationship with the instantaneous mortality hazard, \(\mu_x\):

\[{}_tp_x = e^{-H_x(t)}\qquad(1)\]

where \(H_x(t)\) is the integrated hazard:

\[H_x(t) = \int_0^t\mu_{x+s}ds\qquad(2).\]

Impossibility has often featured in humourous fiction.  From Lewis Carroll's White Queen, who "believed as many as six impossible things before breakfast", to Douglas Adams' Restaurant at the End of the Universe, there is entertainment value in absurdity.

When asked what was most likely to blow a government off-course, Harold Macmillan allegedly replied "Events, dear boy, events!".  Macmillan may not have actually uttered these words (Knowles, 2006, pages 33-34), but there's no denying that unexpected events can derail your plans.  I was recently faced with some unexpected events, albeit in a rather different context.