1 The background to this paper

1.1 Introduction

The aim of this paper is to illustrate, by example, some potential uses of kernel density estimates (KDEs) for data presentation in archaeology. At their simplest, KDEs can be thought of as an alternative to the histogram, which is one of the most commonly used descriptive statistical devices in archaeology. The appearance of a histogram, and hence the archaeological inferences to be drawn from it, can depend on both the interval width used and the starting point of the first interval (e.g. Whallon, 1987). A KDE overcomes the latter defect and results in a smoother diagram that is more useful for comparative purposes. A problem analogous to that of choice of interval width remains, but theory exists to guide this choice and this is discussed. Kernel density estimates have particular advantages, compared to the histogram, for the presentation of two-dimensional data and this is also a major theme of the paper. Some more experimental work with three-dimensional KDEs is reported.

1.2 Why this paper?

The advantages of KDEs compared to the histogram are quite obvious in some cases. They have been the subject of considerable research in the recent statistical literature, but have been little used by archaeologists. A reason for this, apart from the fact that archaeologists may be unaware of the methodology, has probably been the lack of accessible software. This situation is changing, and it is likely that the methodology will become increasingly available in the future. The main aim of this paper is to alert archaeologists to the possibilities of the methodology, and electronic publication seems an ideal medium in that it is suited to the exploitation of colour graphics and animation, as well as permitting far more graphs than conventional publication would allow.

1.3 Structure

The heart of the paper consists of the examples of univariate and bivariate kernel density estimation. These are preceded by non-technical introductions. The two main sections deal with univariate KDEs and bivariate KDEs respectively. Some more experimental work using trivariate KDEs is also discussed. In all of these cases an important consideration is the degree of smoothing to apply to a data set, and this is discussed in the section on choice of window-width . Within each section a number of separate sub-topics, concerning different aspects of presentation, are covered. We have deliberately eschewed a technical presentation. These are available in the bibliography, and two papers of ours that deal with more technical matters can be downloaded as postscript files or obtained from the authors. Computational considerations are also dealt with in a separate section. Our approach uses routines written for the MATLAB package by the first author. These are freely available within the computational considerations section of this paper, and have been successfully used by others. We are, however, conscious that not everyone will have access to suitable hardware or software. We therefore emphasise that the main purpose of the paper is to convince potential users of the usefulness of KDEs as a methodology for the exploration of archaeological data, rather than to "sell" a particular package or approach.


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Last updated: Tue Sep 10 1996