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6. The future

I have no doubt that mathematical modelling will continue to be a useful tool in the archaeologist's kit of 'tactical' problem-solving tools. Even so, for this approach to achieve anything like its full potential will require considerable effort in making archaeologists aware of the value of such approaches, and in training them in their use. This is most likely to come about through general applications that are perceived to have widespread use, such as the Bayesian approach to the interpretation of 'scientific' dating techniques. Paradoxically, the 'difficult' area of Bayesian statistics may prove to be the bridgehead that will open up the field of mathematical modelling to archaeologists, who often seem to have an intuitive 'feel' for it, even though they would not claim to be able to grasp the mathematical complexities (Bayliss, pers. comm.). However, even apparently 'neutral' issues such as specifying the exact form of uninformative prior probabilities can lead to unexpected problems (Steier and Werner 2000; Bronk Ramsey 2000).

While archaeologists have been thinking about, and in some cases applying, mathematical modelling in their work, the world of modelling has not stood still. For example, there has been much research in recent years into the question of the proper selection of models (for example, see Burnham and Anderson 1998). In other words, what are the effects on one's analyses, carried out within a statistical framework, if that framework is itself inappropriate? We can expect this gradually to become an issue in applied fields as well as in theoretical statistics.

Another area where mathematical modelling might impinge on archaeology is that of sampling. Almost all sampling done in archaeology with any pretence of respectability is done under the paradigm of design-based sampling (Thompson and Seber 1996, 5), which stems ultimately from the highly successful approach of Neyman (1934). This makes no assumptions about the distributions of the variables being estimated. A range of alternative strategies, known collectively as model-based sampling (Thompson and Seber 1996, 5), have been discussed within the statistical community, and appear to offer advantages if appropriate models for one's data can be found. The discussion then leads towards consideration of 'robust' designs in case the specification of one's model is less than perfect. If these developments are to impinge on archaeology, thought must be given to the sorts of models that might be appropriate for archaeological data.

The future of the more strategic models is harder to predict. I cannot see the use of non-linear dynamics becoming widespread amongst archaeologists. Nevertheless, there may well be much in it of which they would do well to be aware, for example, the insight it can bring about ways in which change, sometimes sudden, can occur, and about the challenges which it presents to ideas such as 'equilibrium' or 'stability'. If it can help to establish the idea that change is normal and it is the lack of change that requires explanation, it will have done archaeology a service. The use of large-scale simulation models to 'prove' or 'test' a particular view has probably died with the 1970s, and is not likely to return. There is still a role for them in opening up new possibilities of 'how' changes might occur, but whether this role will often be thought to be worth the considerable effort needed to set up such models, remains to be seen. Finally, as a 'borrowing' discipline, we can only wait and see what developments in the disciplines from which we borrow may have relevance for us. And that is impossible to predict.

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