### Auditing Firewalls

#### (Aug 17, 2019)

In a recent blog I discussed the security improvements brought by changing our certification authority, but that isn't our only recent change. Our v2.8 release contained a number of other technology changes and improvements and we'll discuss a couple of them here.

The first was our implementation of a Web Application Firewall (WAF) on all of our services. Just as a network firewall scrutinises and blocks traffic at the network layer, a WAF functions as a gatekeeper higher up the stack, at the level of the web application. A WAF can fully scrutinise the content of http-level requests and block any that violate defined security rules.

We chose the modsecurity WAF as it was the best fit with our existing platform,…

### Fun and games with constraints

#### (Aug 16, 2019)

I'm a statistician so I worry about standard errors just as much as I worry about point estimates. My blog Up close and intimate with the APCI model looked at the effect of different constraints on parameter estimates in models of mortality. This blog looks at the effect of constraints on the standard errors of the parameter estimates. The results for standard errors are equally surprising as those for parameter estimates; we even have an example where a standard error is identically zero. Both sets of results serve to remind us exactly what is meant by not identifiable.

We will illustrate the ideas with the age-period-cohort or APC model fitted to male data from the Office for National Statistics (ONS). We have…

### Resetting Certificates

#### (Aug 14, 2019)

Web site certification supports the key exchange enabling secure encrypted communication between browser clients and server applications. This is why industry giant Google launched a campaign in 2014 that all web applications should use a browser-recognised certificate authority (CA) and offer encrypted access. In practice Google proposes that all website URLs should begin with the encrypted protocol https://, rather than the identifier for the unencrypted alternative protocol http://. While Longevitas applications have always offered only encrypted access, since our version 2.8 release you might have noticed a change in how we certify our web applications and services, and this blog is a brief…

### Seasonal mortality and age

#### (Aug 6, 2019)

In two previous blogs (here and here) I looked at excess winter mortality.  A first glance at the charts shows that the elderly dominate the death counts.  However, the elderly also happen to provide the bulk of deaths at any time of year, so how can we be sure that they are more vulnerable to seasonal variation?

One approach is to look at the numbers of deaths in each age group over a period of a few years.  If we group the deaths by month of occurrence we will expose any seasonal pattern, assuming the population exposures are roughly constant.  If we then standardise these monthly counts by dividing by the count in a reference month (June, say) then we will have percentage fluctuations by month for each age group.  If the…

Tags: season, winter

### The Hermite model of mortality

#### (Jul 8, 2019)

In Richards (2012) I compared seventeen different parametric models for modelling the mortality of a portfolio of UK annuitants.  The best-fitting model, i.e. the one with the lowest AIC, was the Makeham-Beard model:

$\mu_x = \frac{e^\epsilon+e^{\alpha+\beta x}}{1+e^{\alpha+\rho+\beta x}}\qquad(1)$

where $$\mu_x$$ is the force of mortality at age $$x$$ and $$\alpha$$, $$\beta$$, $$\epsilon$$ and $$\rho$$ are parameters to be estimated.  These parameters have interpretations, e.g. $$\beta$$ is broadly the rate at which the force of mortality increases by age on a logarithmic scale, $$e^\epsilon$$ is the constant background rate of mortality and $$e^{-\rho}$$ is the limiting force of mortality…

### The Poisson assumption under the microscope

#### (Jun 7, 2019)

If you read almost any paper on modelling mortality you will find the assumption that the number of deaths follows the Poisson distribution.  Two well-known papers that use this approach are Brouhns et al (2002) and Cairns et al (2009).  The Continuous Mortality Investigation's age-period-cohort-improvements (APCI) model also makes this assumption (Continuous Mortality Investigation, 2016).  In this post I put the Poisson assumption under the microscope.

We use data on UK males from the Human Mortality Database (HMD) downloaded on 10th May 2019.  We have the number of deaths, $$d_{x,y}$$, age $$x$$ last birthday in year $$y$$ and corresponding mid-year population estimates, the central exposures…

Tags: over-dispersion

### The cohort effects that never were

#### (May 20, 2019)

The analysis of cohort effects has long fascinated the actuarial community; these effects correspond to the observation that specific generations can have longevity characteristics different from those of the previous and the following ones. However, Richards (2008) conjectured that these cohort effects might be errors caused by sudden changes in fertility patterns.  Figure 1 shows the specific example of France, although the phenomenon is universal. The most significant fluctuations can be seen when birth rates fall dramatically during periods of war, such as World War I, and then spike afterwards.

Figure 1. Monthly births in France.  Source: Human Fertility Database.

To understand the impact of…

### Mortality Down Under

#### (Apr 21, 2019)

Different countries have different mortality characteristics, and this is true even where countries have similar levels of wealth and development.  However, different countries also have shared mortality characteristics, and one of these is seasonal variation.  Past blogs on this topic have focused on the UK, but I thought it would be time to consider a country new to Information Matrix: Australia.

Figure 1 shows the long-established phenomenon of peak mortality in winter, and low mortality in summer.  The twist is that winter in the Southern Hemisphere is around six months after (or before) the winter in the Northern Hemisphere, so peak winter mortality occurs at a different point in the calendar.

Figure…

Tags: season, winter, cause of death

### Is your mortality model frail enough?

#### (Apr 10, 2019)

Mortality at post-retirement ages has three apparent stages:

1. A broadly Gompertzian pattern up to age 90 (say), i.e. the mortality hazard is essentially linear on a logarithmic scale.
2. The rate of increase in mortality slows down, the so-called "late-life mortality deceleration".
3. The rate of increase slows down to the point where the mortality rate looks like it might be constant above a certain age (110, say).

In my previous blog I demonstrated the power of the Newman hypothesis, namely that low-frequency errors in stated age can cause the patterns in Stage 2 and (especially) Stage 3.  However, the Newman hypothesis is not the only means whereby apparently simple Gompertz mortality turns into something more…

### Diabetes in the driving seat?

#### (Mar 28, 2019)

Those of us with an interest in population mortality find ourselves in proverbially interesting times. Established patterns of accelerating mortality improvements may have ended and we neither know precisely why this may have happened nor what will follow. Increasingly, this development is considered no short-term blip, but a change with longer-term drivers - however, what might those drivers be?

For some, the answers lie in the political sphere: Sir Michael Marmot famously pointed a finger at UK austerity, while in the US influential research considered financial insecurity and the opioid crisis. Other commentators felt austerity was insufficient to explain the patterns observed, which they saw…