Beyond the histogram. Improved approaches to simple data display in archaeology using kernel density estimates
M. J. Baxter, C. C. Beardah · 1996
This paper has deliberately concentrated on univariate examples, which commonly arise in archaeology and where the advantages of kernel density estimates are, we hope, obvious. The MATLAB routines that have been developed can also handle bounded data where, for example, data are non-negative so that the KDE should be zero for negative values, and adaptive estimation (analogous to the use of variable bin-widths) where h can vary and is typically greater in less dense areas of the data space. The most productive extension of the univariate KDE for archaeologists is likely to be to the bivariate case for which histograms, though occasionally presented, are unwieldy and difficult to interpret. The mathematical development is straightforward, although theory for the optimal choice of window-widths is less advanced than that for the univariate case. Baxter and Beardah (1995) have presented a successful application, based on bivariate plotting of the first two principal components from an analysis of glass compositions, in which the existence of three groups was clearly evident. The methodology is most useful for large data sets, where conventional two-dimensional plots are too dense for any patterns to be easily seen. Another potential area of application would be to the analysis of co-ordinates of finds, of the kind that are used in spatial k-means clustering for example (Baxter, 1994, pp. 148-9). Baxter and Beardah (1995) also exploit the use of contouring, based on work by -5 0 5 10 15 20 25 0 0.02 0.04 0.06 0.08 0.1 0.12 Pot diameter (cm)