It is generally assumed that life expectancy in antiquity was considerably shorter than it is now. In the limited number of cases where skeletal or dental age-at-death estimates have been made on adults for whom there are other reliable indications of age, there appears to be a clear systematic trend towards overestimating the age of young adults, and underestimating that of older individuals. We show that this might be a result of the use of regression-based techniques of analysis for converting age indicators into estimated ages. Whilst acknowledging the limitations of most age-at-death indicators in the higher age categories, we show that a Bayesian approach to converting age indicators into estimated age can reduce this trend of underestimation at the older end. We also show that such a Bayesian approach can always do better than regression-based methods in terms of giving a smaller average difference between predicted age and known age, and a smaller average 95-percent confidence interval width of the estimate. Given these observations, we suggest that Bayesian approaches to converting age indicators into age estimates deserve further investigation. In view of the generality and flexibility of the approach, we also suggest that similar algorithms may have a much wider application.

The use of high-power industrial equipment, such as large-scale mixing equipment or a hydrocyclone for separation of particles in liquid suspension, demands careful monitoring to ensure correct operation. The fundamental task of state-estimation for the liquid suspension can be posed as a time-evolving inverse problem and solved with Bayesian statistical methods. In this paper, we extend Bayesian methods to incorporate statistical models for the error that is incurred in the numerical solution of the physical governing equations. This enables full uncertainty quantification within a principled computation-precision trade-off, in contrast to the over-confident inferences that are obtained when all sources of numerical error are ignored. The method is cast within a sequential Monte Carlo framework and an optimised implementation is provided in Python.