A spline primer

(Nov 19, 2021)

A spline is a mathematical function.  They are used wherever flexibility and smoothness are required, from computer-aided design and cartoon graphics, to the graduation of mortality tables (McCutcheon, 1974).  There are numerous different types of spline, but the most common is the spline proposed by Schoenberg (1964).  Figure 1 shows Schoenberg splines of degrees 0-3, all of which start in 2015:

Figure 1. Schoenberg (1964) splines of degree 0-3 with first non-zero value from 2015.

Figure 1 illustrates a number of properties of a single Schoenberg spline:

  • The splines are local functions, and take the value zero outside their domain.
  • The domain of a spline of degree \(bdeg\) spans \(bdeg+2\) knot points.

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Tags: splines

Actuarial cycle time

(Oct 21, 2021)

The ongoing COVID-19 pandemic has introduced millions of ordinary people to some basic aspects of epidemiology, such as the R number to measure the reproductive ability of a virus.  However, there is another aspect to virus reproduction that is possibly even more important: cycle time.  This was pointed out recently by the epidemiologist Larry Brilliant, when he described the Delta variant of SARS-Cov-2 as "the most infectious disease of our lifetimes":

Sometimes we think of measles or chickenpox as the most explosive. What people get wrong, including a lot of my friends, is that they're forgetting about the cycle time. The incubation period of measles and chickenpox are approximately two weeks. The Delta…

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Tags: productivity, software, parallel processing

Build versus buy

(Oct 2, 2021)

In an earlier blog I quoted extensively from "The Mythical Man-Month", a book by the distinguished software engineer Fred Brooks.  My blog was admittedly self-interested(!) when it cited arguments made by Brooks (and others) for when it makes sense to buy software instead of writing it yourself.  However in place of "buying" one could perhaps better write "externally source" - in addition to purchasing (or licensing) purpose-written software, one can also use freely available software.  A good example is R, which itself depends upon other third-party libraries of mathematical subroutines, such as BLAS and LAPACK.

The question of what to build oneself, and what to externally source, is related to the economic…

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Tags: software, ARIMA, survival models, left-truncation

(H)arms race

(Sep 13, 2021)

I'm not a fan of the hyperbolic use of military metaphors in civilian life.  However, in rare cases they do seem appropriate, and the ongoing SAR-Cov-2 pandemic provides an example.  After all, describing a worker as "front-line" seems justified when the occupation carries a materially increased risk of infection and death (SAGE, 2021).

It is often said of military campaigns that the first casualty of battle is your battle plan - the enemy does not stand still, but adapts.  Something similar can be said of the SARS-Cov-2 virus, which undergoes continual evolution in the face of all our efforts to combat it.  However, unlike historical viral pandemics like the Spanish Influenza of 1918-1920, we have some new…

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Tags: coronavirus

No Thanks for the Memory

(Sep 1, 2021)

That there is "no substitute for experience" is a truism, and one that is very tempting to apply wholesale to human immunity. Indeed, we previously touched upon an particular feature of the 1918 Spanish Flu outbreak, the so-called "W-shaped" mortality impact resulting in disproportionate fatalities amongst younger adults in the 20-40 range. Some researchers theorise that older adults must have experienced an earlier influenza infection and thus gained a key immunological advantage over those not around at that time. However, our truism meets a strong challenge with COVID-19. One of the clearest and most robust observations globally is that for those infected by SARS-COV-2, it sucks to be old.

The different…

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Tags: coronavirus, influenza, pandemic, immunosenescence

Modelling mortality shocks

(Aug 16, 2021)

The ongoing coronavirus pandemic has so far produced two mortality shocks in the UK and many other countries.  Unsurprisingly, the extra mortality is also visible in annuity portfolios.  Such mortality spikes create a challenge for actuaries - how do you model a portfolio's mortality experience when the period covered includes one or more pandemic shocks?

Actuaries analyse recent experience data to set a best-estimate basis (future trends or improvements are usually handled as a separate basis item).  However, the presence of a mortality shock creates a risk of upward bias (unless you want to assume that such mortality shocks will regularly re-occur).  One thought might be to remove all deaths with covid-19…

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Tags: coronavirus, mortality shock, season

Buy versus build

(Aug 9, 2021)

If you are in the business of pricing and managing longevity risk, you need software to help you perform your analysis. You have two choices:

  1. Buy in software purpose-written for the task, or
  2. Build the software yourself.

We have been in the business of selling the software in (1) since 2006, so I fall somewhat short of being a disinterested commentator.  However, regarding (2) I recently rediscovered one of the seminal texts on software engineering, namely "The Mythical Man-Month" by Frederick P. Brooks.  Here is what he has to say regarding the decision above:

The most radical possible solution for constructing software is not to construct it at all [...] Even at a cost of $100,000, a purchased piece of software…

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Tags: software

EDS - Enhanced Dedicated Servers

(Aug 4, 2021)

A large part of our service has tradtionally revolved around Dedicated Servers - parallelised instances of our applications running on multi-threaded platforms for a single license holder (in contrast our shared servers offer single-thread performance in a multi-tenant way to multiple license holders, a model that is suitable for only the least demanding use-cases). Our original dedicated server model developed at the beginning of our business, and it was entirely physical, running on Dell 1950 hardware offering a choice of four or eight cores (hardware threads). After we moved our production platform to a virtualised and replicated environment for improved resilience, we retained our four/eight…

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Tags: technology

A Problem of Excess

(May 12, 2021)

Epidemics and pandemics are, by definition, fast-moving and difficult to track. These are the diseases that we couldn't keep a lid on, outbreaks that breached our initial efforts at control. It follows then, that ongoing reporting of such diseases won't be entirely accurate, subject to various limitations imposed by testing and recording protocols. This reality is misused by some who believe that reported impacts are exaggerated and societal responses unjustified, but such a belief runs counter to the evidence. Excess mortality is implacable that way; a sufficient number of unattributed deaths will demand explanation eventually, and even the briefest examination of excess mortality figures during…

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Tags: coronavirus, mortality, pandemic

Deadly Parallels

(Apr 15, 2021)

Ever since the unhappy arrival of the SARS-COV-2 virus, COVID-19 and influenza have been compared for a multiplicity of reasons. I'm guilty of it myself: around the time of the first COVID-19 lockdown, a friend challenged me on why governments would consider the imposition of such extraordinary measures. My argument was simply that authorities presumably feared COVID-19 could become the next Spanish Flu. Of course, making such statements at that time might have been considered overreach, but I cited that once-in-a-century high-fatality pandemic disaster to illustrate why such strong measures could be considered both reasonable and warranted. It was odd then to find that influenza comparisons were just…

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Tags: coronavirus, influenza, pandemic

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