Lost in translation (reprise)

Late last year I drew up a table of actuarial terms and their translation for statisticians.  I had thought that it was a uniquely actuarial trait to use different names compared to other disciplines.  It turns out that statisticians are almost as guilty.  Table 1 shows some common statistical terms in mortality modelling and their description for non-statisticians.

Table 1. Some statistical terms and their definition for mathematicians and engineers.

Statistical term	Notation	Description
hazard function	varies	The instantaneous failure rate.
observed information matrix		The curvature of the log-likelihood function, i.e. the negative of the matrix of second partial derivatives.  This is the same as the negative of the Hessian matrix.
score function		The gradient of the log-likelihood function, i.e. its first partial derivative.

Our non-statistical readers will recognise the origin of the name of this blog.  If we had called it the Hessian, then things would have been very confusing indeed.