Assessing the error on equivalent dose estimates derived from single aliquot regenerative dose measurements

Measurement of the equivalent dose (De) is central to luminescence dating. Single aliquot methods have been developed in the last 10-15 years, first with the description of methods suitable for feldspars (Duller 1995) and subsequently those applicable to quartz (Murray and Wintle 2000, 2003). Such methods have the advantage that they are comparatively rapid, making it feasible to generate replicate determinations of the De, and generally yield De values of greater precision than multiple aliquot methods (e.g. Hilgers et al. 2001). The ability to make replicate measurements of the De is one of the most significant advantages of single aliquot methods since this makes it possible to explicitly assess the distribution of apparent dose. This may be critical to demonstrate whether a sample was well bleached at deposition, and whether it has suffered from post-depositional mixing (e.g. Roberts et al. 1998; Jacobs et al. 2003). A number of approaches have been suggested for both displaying and analyzing dose distributions (Galbraith et al. 1999; Thomsen et al. 2003; Spencer et al 2003; Galbraith 2003), but implicit to all these approaches is the assumption that the uncertainty in the individual De values is known. Variations in De between different grains can be masked if many grains are measured simultaneously in a single aliquot (Wallinga 2002), and thus most analyses designed to study the dose distribution are undertaken on aliquots containing few grains (typically 20-50) or single grains. At this scale of analysis, not only do any variations in De become apparent, but so too do variations in the brightness of individual grains (McFee and Tite 1998; Duller et al. 2000; McCoy et al. 2000). One effect of such variations in brightness is that the precision with which De can be calculated varies from one aliquot to another. As shown by Bailey and Arnold (2006), accurately assessing the error on the De is vital in these situations if any method is used to combine these results that relies upon weighting the results depending upon the accuracy of the individual results (e.g. the Central Age model or Minimum Age model, Galbraith et al. 1999). Sources of uncertainty in the De can be subdivided into random and systematic sources. This paper only deals with random errors associated with the luminescence measurements and then their combination to determine De. Systematic sources of uncertainty, such as errors in the calibration of the beta or gamma source used to irradiate the sample in the laboratory need to be considered after the combination of individual De values. Similarly, there is an additional source of uncertainty in the suitability of the material for use with the SAR procedure; such uncertainty will be material dependent and has been the subject of much discussion by many authors (e.g. Bailey 2000; Murray et al. 2002; Jacobs et al. 2006a). Such issues are likely to become more significant as the luminescence signal gets close to saturation. The aim of this paper is to compare various approaches to estimating the error on individual De values, and provide some data sets that other workers may wish to analyse using their own methods. The paper will focus on examples where the growth is linear, or approximately linear.