Archaeologists frequently use probability distributions and null hypothesis significance testing (NHST) to assess how well survey, excavation, or experimental data align with their hypotheses about the past. Bayesian inference is increasingly used as an alternative to NHST and, in archaeology, is most commonly applied to radiocarbon date estimation and chronology building. This article demonstrates that Bayesian statistics has broader applications. It begins by contrasting NHST and Bayesian statistical frameworks, before introducing and applying Bayes's theorem. In order to guide the reader through an elementary step-by-step Bayesian analysis, this article uses a fictional archaeological faunal assemblage from a single site. The fictional example is then expanded to demonstrate how Bayesian analyses can be applied to data with a range of properties, formally incorporating expert prior knowledge into the hypothesis evaluation process.

The IntCal09 and Marine09 radiocarbon calibration curves have been revised utilizing newly available and updated data sets from 14C measurements on tree rings, plant macrofossils, speleothems, corals, and foraminifera. The calibration curves were derived from the data using the random walk model (RWM) used to generate IntCal09 and Marine09, which has been revised to account for additional uncertainties and error structures. The new curves were ratified at the 21st International Radiocarbon conference in July 2012 and are available as Supplemental Material at www.radiocarbon.org. The database can be accessed at http://intcal.qub.ac.uk/intcal13/.

The Southern Hemisphere SHCal04 radiocarbon calibration curve has been updated with the addition of new data sets extending measurements to 2145 cal BP and including the ANSTO Younger Dryas Huon pine data set. Outside the range of measured data, the curve is based upon the ern Hemisphere data sets as presented in IntCal13, with an interhemispheric offset averaging 43 ± 23 yr modeled by an autoregressive process to represent the short-term correlations in the offset.

High-quality data from appropriate archives are needed for the continuing improvement of radiocarbon calibration curves. We discuss here the basic assumptions behind 14C dating that necessitate calibration and the relative strengths and weaknesses of archives from which calibration data are obtained. We also highlight the procedures, problems, and uncertainties involved in determining atmospheric and surface ocean 14C/12C in these archives, including a discussion of the various methods used to derive an independent absolute timescale and uncertainty. The types of data required for the current IntCal database and calibration curve model are tabulated with examples.

This update on radiocarbon calibration results from the 19th International Radiocarbon Conference at Oxford in April 2006, and is essential reading for all archaeologists. The way radiocarbon dates and absolute dates relate to each other differs in three periods: back to 12400 cal BP, radiocarbon dates can be calibrated with tree rings, and the calibration curve in this form should soon extend back to 18000 cal BP. Between 12400 and 26000 cal BP, the calibration curves are based on marine records, and thus are only a best estimate of atmospheric concentrations. Beyond 26000 cal BP, dates have to be based on comparison (rather than calibration) with a variety of records. Radical variations are thus possible in this period, a highly significant caveat for the dating of middle and lower Paleolithic art, artefacts and animal and human remains.

New radiocarbon calibration curves, IntCal04 and Marine04, have been constructed and internationally ratified to replace the terrestrial and marine components of IntCal98. The new calibration data sets extend an additional 2000 yr, from 0–26 cal kyr BP (Before Present, 0 cal BP = AD 1950), and provide much higher resolution, greater precision, and more detailed structure than IntCal98. For the Marine04 curve, dendrochronologically-dated tree-ring samples, converted with a box diffusion model to marine mixed-layer ages, cover the period from 0–10.5 cal kyr BP. Beyond 10.5 cal kyr BP, high-resolution marine data become available from foraminifera in varved sediments and U/Th-dated corals. The marine records are corrected with site-specific 14C reservoir age information to provide a single global marine mixed-layer calibration from 10.5–26.0 cal kyr BP. A substantial enhancement relative to IntCal98 is the introduction of a random walk model, which takes into account the uncertainty in both the calendar age and the 14C age to calculate the underlying calibration curve (Buck and Blackwell, this issue). The marine data sets and calibration curve for marine samples from the surface mixed layer (Marine04) are discussed here. The tree-ring data sets, sources of uncertainty, and regional offsets are presented in detail in a companion paper by Reimer et al. (this issue).

How and when was northern Europe reoccupied at the end of the last Ice Age? Radiocarbon dates from the earliest post-glacial contexts provide one answer: they offer a sequence in which the regions of Europe, from the Upper Rhine to Britain, saw the return of humans. The authors use Bayesian methods to model a chronology and thus arrive at a sequence with clear assessments of uncertainty.

The first meeting of the IntCal04 working group took place at Queen's University Belfast from April 15 to 17, 2002. The participants are listed as co-authors of this report. The meeting considered criteria for the acceptance of data into the next official calibration dataset, the importance of including reliable estimates of uncertainty in both the radiocarbon ages and the cal ages, and potential methods for combining datasets. This preliminary report summarizes the criteria that were discussed, but does not yet give specific recommendations for inclusion or exclusion of individual datasets.

Archaeological syntheses of western Ecuadorian prehistory have been hampered by a lack of reliable absolute chronologies and detailed cultural sequences for many key areas, one of which is northern Manabí Province, known principally as the territory of the Jama-Coaque cultural tradition. This study presents a seven-phase cultural sequence for the Jama River valley of northern Manabí that spans over 3,600 calendar years. A statistical model relating the successive archaeological phases is established, based on prior knowledge of the stratigraphy and ceramic seriation from key archaeological sites throughout the valley. A Bayesian statistical approach is then employed to calibrate 37 radiocarbon determinations for the purpose of estimating calendar dates for the limits of these phases. Apart from its contribution to the prehistory of a poorly studied area, the analysis illustrates the value of a probabilistic Bayesian approach to radiocarbon calibration, especially when the determinations relate to archaeologically predefined phases. It also demonstrates the dangers of uncritically applying generalized periodization schemes to specific sequences of historical development and highlights the need for reassessing Ecuadorian chronology through more precise interregional correlations.