Splines with parameters that can be explained in words to non-mathematicians

This contribution is based on my programs bspline and frencurv, which are used to generate bases for Schoenberg B-splines and splines parameterized by their values at reference points on the X-axis (presented in STB-57 as insert sg151). The program frencurv ("French curve") makes it possible for the user to fit a model containing a spline, whose parameters are simply values of the spline at reference points on the X-axis. For instance, if I am modeling a time series of daily hospital asthma admissions counts to assess the effect of acute pollution episodes, I might use a spline to model the long-term time trend (typically a gradual long-term increase superimposed on a seasonal cycle), and include extra parameters representing the short-term increases following pollution episodes. The parameters of the spline, as presented with confidence intervals, might then be the levels of hospital admissions, on the first day of each month, expected in the absence of pollution. The spline would then be a way of interpolating expected pollution-free values for the other days of the month. The advantage of presenting splines in this way is that the spline parameters can be explained in words to a non-mathematician (e.g., a medic), which is not easy with other parameterizations used for splines.