Summary
This chapter provides an overview of a topic that is likely to become increasingly important as greater numbers of researchers adopt formal statistical models for constructing chronologies. Other chapters in this volume (1, 2, 3, 10 and 11) use single statistical models, but in the future, as researchers attempt to draw together coherently information from different sources, they will almost certainly develop several alternative models for a single problem. Different statistical models may, however, produce very different interpretations of the same data and thus give rise to conflicting reconstructions of the past. In such situations, we need a robust way to investigate which models are best supported by the data. This chapter outlines recent developments in the application of formal Bayesian model choice techniques to archaeological chronology building and illustrates these tools using two examples, one from absolute and the other from relative chronology building problems. A particular advantage of Bayesian model choice techniques lies in their ability to compare widely different models based on differing assumptions and prior information.
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References
Aitkin, M. (1997). The calibration of P-values, posterior Bayes factors and the AlC from the posterior distribution of the likelihood. Statistics and Computing, 7, 253–261.
Baxter, M. J. (1994). Exploratory multivariate analysis in archaeology. Edinburgh University Press, Edinburgh.
Buck, C. E., Cavanagh, W. G. and Litton, C. D. (1996). Bayesian approach to interpreting archaeological data. John Wiley, Chichester.
Buck, C. E. and Sahu, S. K. (2000). Bayesian models for relative archaeological chronology building. Applied Statistics, 49, 423–440.
Chen, M. H., Shao, Q. M. and Ibrahim, J. G. (2000). Monte Carlo methods in Baye sian computation. Wiley, New York.
DiCiccio, T. J., Kass, R. E., Raftery, A. and Wasserman, L. (1997). Computing Bayes factors by combining simulation and asymptotic approximations. Journal of the American Statistical Association, 92, 903–915.
Geisser, S. and Eddy, W. (1979). A predictive approach to model selection. Journal of the American Statistical Association, 74, 153–160.
Gelfand, A. E. (1996). Model determination using sampling based methods. In W. R. Gilks, S. Richardson and D. J. Spiegelhalter (eds.), Markov chain Monte Carlo in practice, Chapman and Hall.
Gelfand, A. E. and Ghosh, S. (1998). Model choice: a minimum posterior predictive loss approach. Biometrika, 85, 1–11.
Gelfand, A. E. and Smith, A. F. M. (1990). Sampling based approaches to calculating marginal densities. Journal of the American Statistical Association, 85, 398–409.
Gilks, W., Richardson, S. and Spiegelhalter, D. (eds.) (1996). Markov chain Monte Carlo in practice. Chapman and Hall, London.
G6mez Portugal Aguilar, D., Litton, C. D. and O’Hagan, A. (2002). Novel statistical model for a piece-wise linear radiocarbon calibration curve. Radiocarbon, 44, 195–212.
Goodman, L. A. (1986). Some useful extensions of the usual correspondence analysis approach and the usual log linear model approach in the analysis of contingency tables. International Statistical Review, 54, 243–309.
Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82, 711–732.
Jacobi, R. M., Laxton, R. R. and Switsur, V. R. (1980). Seriation and dating of mesolithic sites in southern England. Revue d’Archeotnetrie, 4, 165–173.
Kass, R. E. and Raftery, A. E. (1995). Bayes factors and model uncertainty. Journal of the American Statistical Association, 90, 773–795.
Kendall, D. G. (1971). Seriation from abundance matrices. In F. R. Hodson, D. G. Kendall and P. Tautu (eds.), Mathematics in the archaeological and historical sciences, Edinburgh University Press, Edinburgh, 215–252.
Laud, P. W. and Ibrahim, J. G. (1995). Predictive model selection. Journal of the Royal Statistical Society, 57, 247–262.
Laxton, R. R. (1976). A measure of pre-Q-ness with applications to archaeology. Journal of Archaeological Science, 3, 43–54.
Nicholls, G. and Jones, M. (2001). Radiocarbon dating with temporal order constraints. Applied Statistics, 50, 503–521.
Reece, R. (1994). Are Bayesian statistics useful to archaeological reasoning? Antiquity, 68, 848–850.
Rubin, D. B. (1984). Bayesianly justifiable and relevant frequency calculations for the applied statistician. Annals of Statistics, 12, 1151–1172.
Shennan, S. (1998). Quantifying archaeology. Edinburgh University Press, Edinburgh.
Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and van der Linde, A. (2002). Bayesian measures of model complexity and fit (with discussion). Journal of the Royal Statisti cal Society B, 64, 583–639.
Stuiver, M. K., Reimer, P. J. and Braziunas, T. F. (1998). High-precision radiocarbon age calibration for terrestrial and marine samples. Radiocarbon, 40, 1127–1151.
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Sahu, S.K. (2004). Applications of Formal Model Choice to Archaeological Chronology Building. In: Buck, C.E., Millard, A.R. (eds) Tools for Constructing Chronologies. Lecture Notes in Statistics, vol 177. Springer, London. https://doi.org/10.1007/978-1-4471-0231-1_5
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DOI: https://doi.org/10.1007/978-1-4471-0231-1_5
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