### One small step

#### (Dec 7, 2010)

When fitting mortality models, the foundation of modern statistical inference is the log-likelihood function. The point at which the log-likelihood has its maximum value gives you the maximum-likelihood estimates of your parameters, while the curvature of the log-likelihood tells you about the standard errors of those parameter estimates.

The log-likelihood function is maximised by finding where the gradient is zero. To find this, one requires the first derivatives of the function with respect to each parameter. Similarly, the curvature is measured by the second partial derivatives with respect to each possible pair of parameters. In both cases, one requires either the derivatives themselves, or…