Academic journal article Population

Estimating Age without Measuring It: A New Method in Paleodemography

Academic journal article Population

Estimating Age without Measuring It: A New Method in Paleodemography

Article excerpt

(ProQuest: ... denotes formulae omitted.)

Age, a fundamental concept in demography, cannot be directly measured for most past populations as they did not keep vital statistics. All we can do is to estimate age from biological growth indicators for immature individuals, or ageing for adults, measured on a small number of skeletons belonging to a given population, with the aid of bone or dental remains. Unfortunately, these indicators can give us only a broad range for an individual's age at death because there is no precise relationship between age and bone condition, but only a rather weak correlation.

To advance the study of that correlation, paleodemographers have long been using what are known as "reference" data (Masset, 1971), obtained on sites where it has been possible to determine both the age at death and biological indicator(s) for each individual. These data are described in greater detail in Section I, as are data from the "target" site, where only data on indicators are available. The statistical problem consists in estimating the distribution of ages at death on the target site from data observed there and from reference data. Various methods have been proposed for the purpose over the years. We recall the main developments in Section II, focusing on the most common approach: the discrete case where bone characteristics and ages are distributed into classes. We consider the case where only one biological indicator is observed, but the generalization to several indicators is straightforward. The first hypothesis centres on the conditional probabilities of the ages associated with each indicator value. It is less satisfactory than the second, called "invariance hypothesis", which assumes that the conditional distribution of indicators, at a given age, is constant over time in the periods concerned, at least for a first approximation.(1)

Although the performance of methods proposed earlier has gradually improved, it remains disappointing. The results are often visibly aberrant with respect to prior knowledge and plain common sense. In fact, they tend to be general methods, most of which fail to address all random aspects of the data or the specific characteristics of the problem (we shall see, for example, that a widely used method is borrowed from ichthyology, with a basic model that is formally identical but remains far too general). Given that we are dealing with samples that are often small for an estimation problem marked by intrinsically high instability, it is important to set up a methodology that best incorporates the sum of prior paleodemographic knowledge. The most logical means to this end is a Bayesian method - as suggested in Section III.

The method we propose is Bayesian as commonly understood in statistics. By contrast, certain earlier methods are improperly referred to as Bayesian, for the sole reason that - at some point or other - they make use of Bayes' famous formula. Recall that, unlike a frequentist method in which the unknown parameters are assumed to be fixed, a Bayesian method treats these parameters as random variables. We choose a prior distribution, i.e. before observation, for the parameters, and we determine the posterior distribution, i.e. the distribution revised for a given target site on the basis of data observed at the site. In the prior distribution, we can introduce information preceding the actual data, notably the fact that the probabilities to be estimated reflect a mortality distribution (in some cases, in a specific known environment). We shall also see that, in our problem, it is logical to assume that the reference data supply a prior distribution for certain parameters that are most often deemed to be known - quite unjustifiably, since the data are affected by sampling errors (not to speak of the necessarily approximate nature of the invariance hypothesis).

As shown in Section IV, our method compares very favourably with earlier ones. In Section V, its application is illustrated with two examples. …

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