A parametric model for heterogeneity in paired poisson counts

\Ve present a model for data in the form of match pairs of counts. Our work is motivated by a problem in fission track analysis, where the determination of a crystal age is based on the ratio of counts of spontaneous and induced tracks. It is often reasonable to assume that the counts follow a Poisson distribution but, typically, they are overdispersed and there exists a positive correlation between the numbers of spontaneous and induced tracks at the same crystal. We propose a model that allows for both overdispersion and correlation by assuming that the mean densities follow a bivariate Wishart distribution. Our model is quite general, having the usual negative binomial or Poisson models as special cases. \Ve propose a maximum likelihood estimation method based on a stochastic implementation of the EM algorithm and we derive the asymptotic standard errors of the parameter estimates. vVe illustrate the method by a data set of fission tracks counts in matched areas of zircon crystals

Robust radiocarbon dating of wood samples by high-sensitivity liquid scintillation spectroscopy in the 50–70 kyr age range

Although high-sensitivity liquid scintillation (LS) spectroscopy is theoretically capable of producing finite radiocarbon ages in the 50,000- to 70,000-yr range, there is little evidence in the literature that meaningful dates in this time period have been obtained. The pressing need to undertake calibration beyond 26 kyr has resulted in the regular publication of ¹⁴C results in excess of 50 kyr, yet very little effort has been made to demonstrate their accuracy or precision. There is a paucity of systematic studies of the techniques required to produce reliable dates close to background and the methods needed to assess contamination from either in situ sources or laboratory handling and processing. We have studied the requirements for producing accurate and reliable dates beyond 50 kyr. Laboratory procedures include optimization of LS spectrometers to obtain low and stable non-¹⁴C background count rates, use of low-background counting vials, large benzene volumes, long counting times, and preconditioning of vacuum lines. We also discuss the need for multiple analyses of a suitable material containing no original ¹⁴C (background blank) and the application of an appropriate statistical model to compensate for variability in background contamination beyond counting statistics. Accurate and reproducible finite ages >60 kyr are indeed possible by high-sensitivity LS spectroscopy, but require corroborating background blank data to be defensible

Towards a radiocarbon calibration for oxygen isotope stage 3 using New Zealand kauri (Agathis australis)

It is well known that radiocarbon years do not directly equate to calendar time. As a result, considerable effort has been devoted to generating a decadally resolved calibration curve for the Holocene and latter part of the last termination. A calibration curve that can be unambiguously attributed to changes in atmospheric ¹⁴C content has not, however, been generated beyond 26 kyr cal BP, despite the urgent need to rigorously test climatic, environmental, and archaeological models. Here, we discuss the potential of New Zealand kauri (Agathis australis) to define the structure of the ¹⁴C calibration curve using annually resolved tree rings and thereby provide an absolute measure of atmospheric ¹⁴C. We report bidecadally sampled ¹⁴C measurements obtained from a floating 1050-yr chronology, demonstrating repeatable ¹⁴C measurements near the present limits of the dating method. The results indicate that considerable scope exists for a high-resolution ¹⁴C calibration curve back through OIS-3 using subfossil wood from this source

Ages for the Middle Stone Age of Southern Africa: Implications for Human behavior and Dispersal

The expansion of modern human populations in Africa 80,000 to 60,000 years ago and their initial exodus out of Africa have been tentatively linked to two phases of technological and behavioral innovation within the Middle Stone Age of southern Africa - the Still Bay and Howieson's Poort industries - that are associated with early evidence for symbols and personal ornaments. Establishing the correct sequence of events, however, has been hampered by inadequate chronologies. We report ages for nine sites from varied climatic and ecological zones across southern Africa that show that both industries were short-lived (5000 years or less), separated by about 7000 years, and coeval with genetic estimates of population expansion and exit times. Comparison with climatic records shows that these bursts of innovative behavior cannot be explained by environmental factors alone

Statistics for Fission-Track Thermochronology

This chapter introduces statistical tools to extract geologically meaningful information from fission-track (FT) data using both the external detector and LA-ICP-MS methods. The spontaneous fission of 238U is a Poisson process resulting in large single-grain age uncertainties. To overcome this imprecision, it is nearly always necessary to analyse multiple grains per sample. The degree to which the analytical uncertainties can explain the observed scatter of the single-grain data can be visually assessed on a radial plot and objectively quantified by a chi-square test. For sufficiently low values of the chi-square statistic (or sufficiently high p values), the pooled age of all the grains gives a suitable description of the underlying ‘true’ age population. Samples may fail the chi-square test for several reasons. A first possibility is that the true age population does not consist of a single discrete age component, but is characterised by a continuous range of ages. In this case, a ‘random effects’ model can constrain the true age distribution using two parameters: the ‘central age’ and the ‘(over)dispersion’. A second reason why FT data sets might fail the chi-square test is if they are underlain by multimodal age distributions. Such distributions may consist of discrete age components, continuous age distributions, or a combination of the two. Formalised statistical tests such as chi-square can be useful in preventing overfitting of relatively small data sets. However, they should be used with caution when applied to large data sets (including length measurements) which generate sufficient statistical ‘power’ to reject any simple yet geologically plausible hypothesis

Minority environmental activism in Britain: From brixton to the lake district

Historically, the British environmental movement has been devoid of minority participation, but this is changing very slowly, with the emergence of ethnic minority environmental groups and multiracial environmental alliances. These groups have argued that ethnic minorities have little or no access to public funds earmarked for countryside and wildlife preservation issues. They argue that white environmental organizations do not pay attention to the needs of inner-city minority residents and minority access to the countryside. Increased access, community improvement and beautification projects, environmental education, youth training, community garden projects, and issues of environmental racism are all foci of ethnic minority environmental movements. While some white environmentalists have been supportive of them, others have been uncomfortable with them or even hostile to their existence.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43549/1/11133_2004_Article_BF00990102.pd

Variability in quartz OSL signals caused by measurement uncertainties: Problems and solutions

We simulated the variability in measured quartz optically stimulated luminescence (OSL) signals and dose response curves (DRCs) caused by measurement uncertainties, including counting statistics and instrumental irreproducibility. We find that these measurement errors can give rise to large variations in the observed luminescence signal and contribute to among-aliquot or among-grain scatter in DRCs and equivalent dose (De) values. Different measurement systems (i.e., luminescence readers) may have different counting statistics properties and, hence, may exhibit differing extents of variation in the observed OSL signal, even for the same sample. Our simulation shows that the random measurement uncertainties may result in some grains or aliquots being ¿saturated¿ (that is, the measured natural signal is consistent with, or lies above, the saturation level of the measured DRC) and that the rejection of these ¿saturated¿ grains may result in a truncated De distribution, with De underestimation for samples with natural doses close to saturation (e.g., twice the characteristic saturation dose, D0). We propose a new method to deal with this underestimation problem, in which standardised growth curves (SGCs) are established and the weighted-mean natural signal (Ln/Tn) from all measured grains is projected on to the corresponding SGCs to determine De. Our simulation results show that this method can produce reliable De estimates up to 5D0, which is far beyond the conventional limit of ¿2D0 using the standard SAR procedure

Robust radiocarbon dating of wood samples by high-sensitivity liquid scintillation spectroscopy in the 50-70 Kyr age range

Although high-sensitivity liquid scintillation (LS) spectroscopy is theoretically capable of producing finite radiocarbon ages in the 50,000- to 70,000-yr range, there is little evidence in the literature that meaningful dates in this time period have been obtained. The pressing need to undertake calibration beyond 26 kyr has resulted in the regular publication of 14C results in excess of 50 kyr, yet very little effort has been made to demonstrate their accuracy or precision. There is a paucity of systematic studies of the techniques required to produce reliable dates close to background and the methods needed to assess contamination from either in situ sources or laboratory handling and processing. We have studied the requirements for producing accurate and reliable dates beyond 50 kyr. Laboratory procedures include optimization of LS spectrometers to obtain low and stable non-14C background count rates, use of low-background counting vials, large benzene volumes, long counting times, and preconditioning of vacuum lines. We also discuss the need for multiple analyses of a suitable material containing no original 14C (background blank) and the application of an appropriate statistical model to compensate for variability in background contamination beyond counting statistics. Accurate and reproducible finite ages >60 kyr are indeed possible by high-sensitivity LS spectroscopy, but require corroborating background blank data to be defensible

An improved OSL chronology for the Still Bay layers at Blombos Cave, South Africa: further tests of single-grain dating procedures and a re-evaluation of the timing of the Still Bay industry across southern Africa

This paper presents a series of new single-grain optically stimulated luminescence (OSL) ages for the Still Bay at Blombos Cave, South Africa, and compares them to previously published OSL, thermoluminescence (TL) and electron-spin resonance (ESR) ages for this site. Details are provided about the measurement and analytical procedures, including a discussion of the characteristics of the OSL signals of individual quartz grains. This forms the basis for further investigations into the sensitivity of the equivalent dose (De) estimates to a range of different analytical approaches, including changes in the size of the test dose, the choice of signal integration interval, the subtraction of an appropriate background, and isolation of the most light-sensitive (‘fast’) component of quartz OSL. We also report the results of an inter-operator test of De determination using seven new samples from Blombos Cave, and demonstrate the reproducibility of results obtained for two samples that had been dated previously at another laboratory and were measured and analysed again in this study. Together, these tests validate the robustness of the Blombos Cave single-grain OSL age estimates to a variety of alternative OSL dating procedures. We have incorporated, for the first time, these ages for Blombos Cave into a data set of all single-grain OSL ages for Still Bay and Howieson\u27s Poort sites across southern Africa, and have used a statistical model to re-evaluate the timing and duration of the Still Bay industry. We calculate the most plausible start and end dates of the Still Bay as 72.2 ka and 71.3 ka, respectively – amounting to a duration of 0.9 ka – and estimate (with conventional 95% confidence) that this industry began no earlier than 75.5 ka, ended no later than 67.8 ka and lasted no longer than 6.6 ka