Information Matrix

In the course of a recent investigation, with my colleagues Dr Oytun Haçarız and Professor Torsten Kleinow, a key parameter was the mortality rate of persons suffering from Hypertrophic Cardiomyopathy (HCM), an inherited heart disorder characterized by thickening of the left ventricular muscle wall.  It is quite rare, so precision is not to be expected, and indeed an annual mortality rate of 1% \((q_x=0.01)\), independent of age \(x\), is widely cited.  I

Interest rates and gilt yields are critical drivers of pension-scheme reserving and bulk-annuity pricing.  However, many UK pension schemes self-insure when it comes to economic risks, with Liability Driven Investment (LDI) a common approach.  This makes the turmoil in the UK Gilts market in Autumn 2022 of particular interest.  Daily movements of 10-20 standard deviations arose as the

One interesting aspect of maximum-likelihood estimation is the common behaviour of estimators, regardless of the nature of the data and model.  Recall that the maximum-likelihood estimate, \(\hat\theta\), is the value of a parameter \(\theta\) that maximises the likelihood function, \(L(\theta)\), or the log-likelihood function, \(\ell(\theta)=\log L(\theta)\).  By way of example, consider the following three single-parameter distributions:

In mortality forecasting work we often deal with downward trends.  It is often tempting to jump to the assumption of a linear trend, in part because this makes for easier mathematics.  However, real-world phenomena are rarely purely linear, and the late Iain Currie advocated linear adjustment as means of judging linear-seeming patterns.  This involves calculating a line between the first and last points, and deducting the line value at ea

In my previous blog I showed how univariate stochastic mortality models, like the Lee-Carter and APC models, can be robustified to cope with data affected by the covid-19 pandemic.  Such robustification is necessary because outliers, such as the 2020 experience, bias parameter estimates and affect value-at-risk (VaR) capital requirements.  Kleinow & Richards (2016) showed how one-year VaR-style capital requirements are heavily de

The covid-19 pandemic led to high levels of mortality in many countries in 2020. Figure 1 shows that the number of deaths in England & Wales in 2020 was an outlier compared to preceding years.

Figure 1. Total deaths by calendar year for females in England & Wales. Source: HMD data, ages 50–105.

In Richards (2022) I proposed a simple real-time mortality tracker that can be implemented in a spreadsheet or R. The tracker is useful for exploratory analysis, spotting data-quality issues and communication with non-specialists. To recap, we require just three items of data:

It is with great sadness that we note the passing of our long-term collaborator, Dr. Iain D. Currie, on 24th May 2022.

In criminal investigation, it is well known that passing time obscures the facts, making what happened more difficult to discern. Eventually, the case turns cold - unlikely to be solved unless we discover new evidence. In some ways for over a century, epidemiologists have been dealing with just such a cold case, picking through the rubble of the 1918 Influenza pandemic and trying to make sense of what they find. But as we will see, debate continues in a number of areas.