Bayesian classification of Neolithic tools

The classification of Neolithic tools by using cluster analysis enables archaeologists to understand the function of the tools and the technological and cultural conditions of the societies that made them. In this paper, Bayesian classification is adopted to analyse data which raise the question whether the observed variability, e.g. the shape and dimensions of the tools, is related to their use. The data present technical difficulties for the practitioner, such as the presence of mixed mode data, missing data and errors in variables. These complications are overcome by employing a finite mixture model and Markov chain Monte Carlo methods. The analysis uses prior information which expresses the archaeologist's belief that there are two tool groups that are similar to contemporary adzes and axes. The resulting mixing densities provide evidence that the morphological dimensional variability among tools is related to the existence of these two tool groups.

[1]  J. Gower A General Coefficient of Similarity and Some of Its Properties , 1971 .

[2]  Michael A. West,et al.  Deconvolution of Mixtures in Analysis of Neural Synaptic Transmission , 1994 .

[3]  C. Robert,et al.  Estimation of Finite Mixture Distributions Through Bayesian Sampling , 1994 .

[4]  B. S. Everitt,et al.  A finite mixture model for the clustering of mixed-mode data , 1988 .

[5]  J. Zidek,et al.  Inference for a covariance matrix , 1994 .

[6]  M. West,et al.  A Bayesian method for classification and discrimination , 1992 .

[7]  P. Green,et al.  On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion) , 1997 .

[8]  J. Besag,et al.  Bayesian Computation and Stochastic Systems , 1995 .

[9]  Adrian F. M. Smith,et al.  Bayesian computation via the gibbs sampler and related markov chain monte carlo methods (with discus , 1993 .

[10]  D. Binder Bayesian cluster analysis , 1978 .

[11]  P. Dellaportas,et al.  BAYESIAN ANALYSIS OF ERRORS-IN-VARIABLES REGRESSION MODELS , 1995 .

[12]  Bradley P. Carlin,et al.  Markov Chain Monte Carlo conver-gence diagnostics: a comparative review , 1996 .

[13]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[14]  Walter R. Gilks,et al.  Bayesian model comparison via jump diffusions , 1995 .

[15]  A. Raftery,et al.  How Many Iterations in the Gibbs Sampler , 1991 .

[16]  G. Roberts,et al.  Updating Schemes, Correlation Structure, Blocking and Parameterization for the Gibbs Sampler , 1997 .

[17]  J. Leblanc THÈSE DE 3ÈME CYCLE , 1978 .

[18]  B. S. Everitt,et al.  The clustering of mixed-mode data: A comparison of possible approaches , 1990 .

[19]  A. D. Gordon,et al.  Classification : Methods for the Exploratory Analysis of Multivariate Data , 1981 .

[20]  P. Green Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

[21]  A. Moundrea-Agrafioti,et al.  Outils tranchants thessaliens en pierre polie : un réexamen de la typologie de Christos Tsountas , 1991 .

[22]  David J. Hand,et al.  Discrimination and Classification , 1982 .

[23]  G. McLachlan Discriminant Analysis and Statistical Pattern Recognition , 1992 .

[24]  A. D. Gordon A Review of Hierarchical Classification , 1987 .

[25]  Wojtek J. Krzanowski,et al.  Mixture separation for mixed-mode data , 1996, Stat. Comput..

[26]  A. D. Gordon Constructing dissimilarity measures , 1990 .

[27]  Adrian F. M. Smith,et al.  Bayesian Analysis of Constrained Parameter and Truncated Data Problems , 1991 .

[28]  Kerrie Mengersen,et al.  [Bayesian Computation and Stochastic Systems]: Rejoinder , 1995 .

[29]  Brian Everitt,et al.  Principles of Multivariate Analysis , 2001 .

[30]  Charles J. Geyer,et al.  Practical Markov Chain Monte Carlo , 1992 .

[31]  A. F. Smith,et al.  Statistical analysis of finite mixture distributions , 1986 .

[32]  B. Everitt,et al.  Finite Mixture Distributions , 1981 .

[33]  S. Chib,et al.  Bayesian analysis of binary and polychotomous response data , 1993 .

[34]  Geoffrey J. McLachlan,et al.  Mixture models : inference and applications to clustering , 1989 .