Section: Application Domains

Archaeology

We have been working since 2011 on the construction of new Bayesian approach for chronological modeling: this is an important issue in archaeology and paleo-environmental sciences. The archaeologists base their interpretations on a wide range of sources of information. A priori knowledge about the parameters of the model is often available, and so it should be considered along with the model and the data. This motivates the Bayesian choice.

In our case the data are the measurements $M_i$ provided by dating laboratories e.g. 14C). The prior information contains historical evidence (e.g. an event must have occurred between two calendar dates,..) or geological information (e.g. a stratigraphic information,..). All the measurements require a calibration step to be converting into calendar date.

Tools for Constructing Chronologies

The aim is to provide probabilistic estimation of a chronology; a crucial aspect is to obtain a robust approach with respect to outliers due to the sampling in the field or the measurement process in the laboratory.

The solution proposed in [7], [6] is based on the "event model'. We define the Event as the date $\theta$ of an archeological context determined from a collection of contemporaneous artifacts. The model with random effect can be written as follows

where $g_i$ is the calibration function and $({\rho }_1,...,{\rho }_n,{\lambda }_1,...,{\lambda }_n)$ are iid standard Gaussian random variables. The random variables ${\left({\lambda }_i\right)}_i$ and ${\left({ϵ}_i\right)}_i$ are interpreted as follows :

• $S_i{\rho }_i$ represents the experimental error provided by the laboratory and the calibration step.

• ${\sigma }_i{\lambda }_i$ represents the irreducible error between $t_i$ and $\theta$ due to sampling problems external to the laboratory

In [7], [6], we show the ability of the variance ${\sigma }_i^2$ to take large values, in order to automatically penalize an outlier.

To enrich the chronological modelling, we wish to incorporate archaeological “phases”. Contrary to an “event”, a phase suggests duration. The objective is then to estimate the parameters that characterize the phase (beginning /end/duration), and then to develop Bayesian tests on the duration of the phase or the existence of a gap (hiatus) between two phases.

Calibration

The dating processes provide measurements, which are converted into calendar dates using calibration reference curves. We plan to explore issues related to calibration for different dating methods.

Optically stimulated luminescence (OSL) dating is a quantitative dating method to determine the time of last exposure of sand and silt to sunlight. Our aim is to complete the model constructed in [2] in order to obtain an OSL age determination.

We generally observe a overestimation of the age of a sample by OSL dating. This can be explaining by an insufficient resetting of the optically stimulated luminescence signal prior to sediment deposition. Therefore detection of so-called poor bleaching is of prime importance in OSL dating.