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ABOUT THIS COLLECTION

Radiocarbon is the main international journal of record for research articles and date lists relevant to 14C and other radioisotopes and techniques used in archaeological, geophysical, oceanographic, and related dating.

This archive provides access to Radiocarbon Volumes 1-54 (1959-2012).

As of 2016, Radiocarbon is published by Cambridge University Press. The journal is published quarterly. Radiocarbon also publishes conference proceedings and monographs on topics related to fields of interest. Visit Cambridge Online for new Radiocarbon content and to submit manuscripts.

ISSN: 0033-8222

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Recent Submissions

  • ZAGRADA—The New Zagreb Radiocarbon Database

    Porter, Antun; Obelić, Bogomil; Krajcar Bronić, Ines (Department of Geosciences, The University of Arizona, 2010-01-01)
    After introducing the liquid scintillation counting (LSC) method and graphite target preparation for accelerator mass spectrometry (AMS) measurements in the Zagreb Radiocarbon Laboratory, the existing database software designed only for gas proportional counting (GPC) (using a DOS operating system) could not satisfy the requirements for parallel conduction of several techniques. This has been enabled recently by the development of the new relational database ZAGRADA, which--using SQL scripts and constraints defined by primary and foreign keys--enforces high data integrity and provides better performances in data filtering and sorting. The structural scheme of this database conceptually comprises 4 basic modules with data on the samples, chemical pretreatment and preparation, measurements and data on the final results. A user-friendly graphical user interface has been designed to perform various actions and data manipulation to the database. The implementation of a new database for 14C samples has significant contribution to scientific research performed in the Radiocarbon and Tritium Laboratory and to quality assurance and quality control, and will enable better and easier communication with customers.
  • Variability of Dissolved Inorganic Radiocarbon at a Surface Site in the Northeast Pacific Ocean

    Druffel, Ellen R. M.; Beaupré, Steven; Griffin, Sheila; Hwang, Jeomshik (Department of Geosciences, The University of Arizona, 2010-01-01)
    We report radiocarbon measurements of dissolved inorganic carbon (DIC) in surface water samples collected daily during 12 cruises to Station M in the northeast Pacific off central California. Individual surface ∆14C values ranged from 22 to 70 over 10 yr. Variability of average cruise values is highest during winter likely due to increased mixing. A general decrease of ∆14C values was observed at a rate of about 3 per year between 1994 and 2004, about half of that in atmospheric CO2 during this period (Levin and Kromer 2004). The ∆14C results ranged from 2-18 during individual cruises and were often significantly larger than the total uncertainty for individual measurements (3.9). This indicates that a single ∆14C result from a surface site is not sufficient to capture the true variability of ∆14C in the surface ocean.
  • Wiggle-Match Dating of Wooden Samples from Iron Age Sites in Northern Italy

    Quarta, G.; Pezzo, M. I.; Marconi, S.; Tecchiati, U.; D'Elia, M.; Calcagnile, L. (Department of Geosciences, The University of Arizona, 2010-01-01)
    Archaeological excavations carried out at the sites of Laion/Lajen (Bolzano/Bozen) and Stufles-Oberegger (Bressanone/Brixen) in northern Italy uncovered well-preserved wooden samples in cultural layers archaeologically dated to the Iron Age. From the 2 sites, different wooden samples were recovered that were well preserved enough to allow clear identification of the tree species and of the ring structure. Among the different wooden samples, 2 were selected for radiocarbon analyses: from Laion/Lajen, a beam with an unbroken sequence of 158 rings; from Stufles-Oberegger, a combusted trunk with a sequence of 217 rings. Both samples were identified as Larix decidua species. From each sequence, single rings were selected and submitted for accelerator mass spectrometry (AMS) 14C dating analysis at CEDAD. Conventional 14C ages were then calibrated to calendar ages using the IntCal04 atmospheric data set, while the statistical constraints resulting from the defined ring sequence were used to develop a wiggle-matching approach by making use of the Bayesian analysis functions available in OxCal. The obtained results are an important contribution in refining the chronology of the studied sites.
  • Turnover Rate of Soil Organic Matter and Origin of Soil 14CO2 in Deep Soil from a Subtropical Forest in Dinghushan Biosphere Reserve, South China

    Ding, P.; Shen, C. D.; Wang, N.; Yi, W. X.; Ding, X. F.; Fu, D. P.; Liu, K. X.; Zhou, L. P. (Department of Geosciences, The University of Arizona, 2010-01-01)
    This paper examines the carbon isotopes (13C, 14C) of soil organic carbon (SOC) and soil CO2 from an evergreen broadleaf forest in southern China during the rainy season. The distribution of SOC 13C, and SOC content with depth, exhibits a regular decomposition of SOC compartments with different turnover rates. Labile carbon is the main component in the topsoil (0-12 cm) and has a turnover rate between 0.1 and 0.01 yr-1. In the middle section (12-35 cm), SOC was mainly comprised of mediate carbon with turnover rates ranging between 0.01 and 0.025. Below 35 cm depth (underlayer section), the SOC turnover rate is slower than 0.001 yr-1, indicating that passive carbon is the main component of SOC in this section. The total production of humus-derived CO2 is 123.84 g C m-2 yr-1, from which 88% originated in the topsoil. The middle and underlayer sections contribute only 10% and 2% to the total humus-derived CO2 production, respectively. Soil CO2 13C varies from -24.7 to -24.0, showing a slight isotopic depth gradient. Similar to soil CO2 13C, ∆14C values, which range from 100.0 to 107.2, are obviously higher than that of atmospheric CO2 (60-70) and SOC in the middle and underlayer section, suggesting that soil CO2 in the profile most likely originates mainly from SOC decomposition in the topsoil. A model of soil CO2 ∆14C indicates that the humus-derived CO2 from the topsoil contributes about 65-78% to soil CO2 in each soil gas sampling layer. In addition, the humus-derived CO2 contributes ~81% on average to total soil CO2 in the profile, in good agreement with the field observation. The distribution and origin of soil 14CO2 imply that soil CO2 will be an important source of atmospheric 14CO2 well into the future.
  • Update on the Performance of the SUERC In Situ Cosmogenic 14C Extraction Line

    Fulöp, R. H.; Naysmith, P.; Cook, G. T.; Fabel, D.; Xu, S.; Bishop, P. (Department of Geosciences, The University of Arizona, 2010-01-01)
    In this paper, we describe improvements to the in situ cosmogenic radiocarbon extraction system at SUERC made since 2004, highlighting the factors that potentially control the reduction of analytical variability. We also present new results on system blanks and of measurements of in situ 14C in shielded quartz and a surface quartz sample used at the University of Arizona as an in situ 14C standard (PP-4). The SUERC in situ 14C extraction system was built in 2001 and is based on a combustion technique following the design of the extraction system at the University of Arizona. Our preliminary results suggest that the continuous running of the extraction system and the monitoring of gas collecting time and of the temperature of the cryogenic traps used in the gas cleaning steps are key to maintaining low and stable system blanks. Our latest average system blank is 2.02 +/- 0.23 x 105 14C atoms. This is consistent with those recently published by the University of Arizona and ETH in situ 14C labs. Measurements of in situ 14C concentrations in sample PP-4 yield an average of 3.82 +/- 0.23 x 105 atoms g-1 quartz, again consistent with published values.
  • Using car4ams, the Bayesian AMS Data Analysis Code

    Palonen, V.; Tikkanen, P.; Keinonen, K. (Department of Geosciences, The University of Arizona, 2010-01-01)
    The Bayesian CAR (continuous autoregressive) model for accelerator mass spectrometry (AMS) data analysis delivers uncertainties with less scatter and bias. Better detection and estimation of the instrumental error of the AMS machine are also achieved. Presently, the main disadvantage is the several-hour duration of the analysis. The Markov chain Monte Carlo (MCMC) program for CAR model analysis, car4ams, has been made freely available under the GPL license. Included in the package is an R program that analyzes the car4ams output and summarizes the results in graphical and spreadsheet formats. We describe the main properties of the CAR analysis and the use of the 2 parts of the program package for radiocarbon AMS data analysis.
  • Timing of the Landslide-Dammed Lake Triggered by Earthquake, at Toyama River, Central Japan

    Goto, Akiko S.; Muramatsu, Takeshi; Teraoka, Yoshiji (Department of Geosciences, The University of Arizona, 2010-01-01)
    Huge landslides triggered by strong earthquakes or torrential rains can result in unstable natural dams that pose serious risks to humans. In this study, we attempt to document the age of an ancient earthquake that produced a landslide-dammed lake. A buried forest found in the Toyama River area of the southern Nagano Prefecture, central Japan, provides evidence of this event. The dammed lake formation has been previously estimated to have occurred in AD 714. However, the age of the dam and the way it was formed have never been directly determined. To determine the position and timing of the landslide dam, we analyzed the radiocarbon content of branches and wood fragments from a brecciated deposit. We show that the 14C dating method is suitable for clarifying the timing of burial for a variety of trees, although the method does not produce a narrow age for the event. In addition to the dating, we determined the landslide dam's position and reconstructed the formation of the lake.
  • Tree-Ring Dating and AMS Wiggle-Matching of Wooden Statues at Neunggasa Temple in South Korea

    Park, Won-Kyu; Kim, Yojung; Jeong, Ah-Reum; Kim, Sang-Kyu; Oh, Jung-Ae; Park, Suh-Young; Cho, Sunil; Park, Gyujun; Seo, Jeong-Wook (Department of Geosciences, The University of Arizona, 2010-01-01)
    This paper reports the results of tree-ring dating and accelerator mass spectrometry (AMS) wiggle-matching for wooden Buddhist statues stored at the Eungjindang Hall of Neunggasa Temple, South Korea. Among 23 statues, 10 were successfully dated by tree rings. The cutting date of logs used for the statues was determined as some time between late fall 1684 and early spring 1685 when the bark ring (AD 1684) completed latewood formation. The 95.4% confidence interval of a radiocarbon date (cal AD 1688-1713, 2 ), which was obtained by wiggle-matching 7 samples of a statue, is similar to the dendro-date (AD 1684). A historical document recorded that the statues in the Eungjindang of Neunggasa were dedicated in July 1685. The dendro-date and written record indicate that Eungjindang statues were made within 3-8 months after log cutting. This seems rather short if we consider the period required for natural drying to avoid defects such as cracking and crooking.
  • The Passage of the Bomb Radiocarbon Pulse into the Pacific Ocean

    Jenkins, William J.; Elder, Kathryn L.; McNichol, Ann P.; Von Reden, Karl (Department of Geosciences, The University of Arizona, 2010-01-01)
    We report and compare radiocarbon observations made on 2 meridional oceanographic sections along 150 degrees W in the South Pacific in 1991 and 2005. The distributions reflect the progressive penetration of nuclear weapons-produced 14C into the oceanic thermocline. The changes over the 14 yr between occupations are demonstrably large relative to any possible drift in our analytical standardization. The computed difference field based on the gridded data in the upper 1600 m of the section exhibits a significant decrease over time (approaching 40 to 50 in ∆14C) in the upper 200-300 m, consistent with the decadal post-bomb decline in atmospheric 14C levels. A strong positive anomaly (increase with time), centered on the low salinity core of the Antarctic Intermediate Water (AAIW), approaches 50-60‰ in ∆14C, a clear signature of the downstream evolution of the 14C transient in this water mass. We use this observation to estimate the transit time of AAIW from its "source region" in the southeast South Pacific and to compute the effective reservoir age of this water mass. The 2 sections show small but significant changes in the abyssal 14C distributions. Between 1991 and 2005, ∆14C has increased by 9 below 2000 m north of 55 degrees S. This change is accompanied overall by a modest increase in salinity and dissolved oxygen, as well as a slight decrease in dissolved silica. Such changes are indicative of greater ventilation. Calculation of "phosphate star" also indicates that this may be due to a shift from the Southern Ocean toward North Atlantic Deep Water as the ventilation source of the abyssal South Pacific.
  • The Effect of Storage on the Radiocarbon, Stable Carbon and Nitrogen Isotopic Signatures and Concentrations of Riverine DOM

    Gulliver, P.; Waldron, S.; Scott, E. M.; Bryant, C. L. (Department of Geosciences, The University of Arizona, 2010-01-01)
    Chemical preservatives (e.g. mercuric chloride) are routinely added to freshwater samples to prevent biological activity compromising the isotopic signature of dissolved organic matter (DOM) with time. However, alternative preservation methods are needed due to regulations restricting the use of preservatives with potentially adverse environmental and health impacts, rendering such additions unviable. This study investigates whether a non-chemical storage method is sufficient to maintain the radiocarbon and stable carbon and nitrogen signatures of freshwater DOM from a low order river system draining a peaty catchment. Some 50 L of stream water were collected in 1 plastic carbuoy and, within 24 hr, 1-L aliquots were transferred to acid-washed plastic bottles. Five aliquots were analyzed immediately to determine the baseline values for 14C (pMC), 13C (VPDB), 15N (AIR), %C (mg L-1), and %N (mg L-1). Of the remaining subsamples, 20 were frozen and a further 20 refrigerated at 4 C. After 7, 30, 90, and 180 days, 5 frozen and 5 refrigerated aliquots were analyzed in the same manner as the baseline aliquots. Analysis of the results shows that there is no statistically significant interaction between the variables storage method or length of storage for any of the determinants. Storage method has a statistically significant effect on 14C (pMC) and [C] (mg L-1). Length of storage has a statistically significant effect on 13C (VPDB), [C] (mg L-1), and [N] (mg L-1) values. Neither storage method nor length of storage appear to have a statistically significant effect on 15N (AIR) values.
  • The Fifth International Radiocarbon Intercomparison (VIRI): An Assessment of Laboratory Performance in Stage 3

    Scott, E. Marian; Cook, Gordon T.; Naysmith, Philip (Department of Geosciences, The University of Arizona, 2010-01-01)
    Proficiency testing is a widely used, international procedure common within the analytical chemistry community. A proficiency trial (which VIRI is) often follows a standard protocol, including analysis that is typically based on zscores, with one key quantity, p. From a laboratory intercomparison (sometimes called a proficiency trial), we hope to gain an assessment of accuracy (in this case, from dendro-dated samples), laboratory precision (from any duplicate samples), and generally, an overall measure of performance, including measurement variability and hence realistic estimates of uncertainty. In addition, given our stated aim of creating an archive of reference materials, we also gain a determination of consensus values for new reference materials. VIRI samples have been chosen to deliver these objectives and the sample ages included in the different stages, by design, spanned modern to background. With regard to pretreatment, some samples required intensive pretreatment (e.g. bone), while others required none (e.g. cellulose and humic acid). Sample size was not optimized, and indeed some samples were provided solely for accelerator mass spectrometry (AMS) measurement. In this sense, VIRI presented a more challenging exercise than previous intercomparisons, since by its design in stages, one can explore improvements (or deteriorations) over time in laboratory performance. At each stage, more than 50 laboratories have participated, with an increasing demographic shift towards more AMS and fewer radiometric laboratories.
  • Temporal and Spatial Variations in Freshwater 14C Reservoir Effects: Lake Mývatn, Northern Iceland

    Ascough, P. L.; Cook, G. T.; Church, M. J.; Dunbar, E.; Einarsson, Á.; McGovern, T. H.; Dugmore, A. J.; Perdikaris, S.; Hastie, H.; Friðoriksson, A.; et al. (Department of Geosciences, The University of Arizona, 2010-01-01)
    Lake Mvatn is an interior highland lake in northern Iceland that forms a unique ecosystem of international scientific importance and is surrounded by a landscape rich in archaeological and paleoenvironmental sites. A significant freshwater reservoir effect (FRE) has been identified in carbon from the lake at some Viking (about AD 870-1000) archaeological sites in the wider region (Mvatnssveit). Previous accelerator mass spectrometry (AMS) measurements indicated this FRE was about 1500-1900 14C yr. Here, we present the results of a study using stable isotope and 14C measurements to quantify the Mvatn FRE for both the Viking and modern periods. This work has identified a temporally variable FRE that is greatly in excess of previous assessments. New, paired samples of contemporaneous bone from terrestrial herbivores and omnivores (including humans) from Viking sites demonstrate at least some omnivore diets incorporated sufficient freshwater resources to result in a herbivore-omnivore age offset of up to 400 14C yr. Modern samples of benthic detritus, aquatic plants, zooplankton, invertebrates, and freshwater fish indicate an FRE in excess of 5000 14C yr in some species. Likely geothermal mechanisms for this large FRE are discussed, along with implications for both chronological reconstruction and integrated investigation of stable and radioactive isotopes.
  • Table of Contents

    Department of Geosciences, The University of Arizona, 2010-01-01
  • Studies on the Preparation of Small 14C Samples with an RGA and 13C-Enriched Material

    Liebl, Jakob; Avalos Ortiz, Roswitha; Golser, Robin; Handle, Florian; Kutschera, Walter; Steier, Peter; Wild, Eva Maria (Department of Geosciences, The University of Arizona, 2010-01-01)
    The minimum size of radiocarbon samples for which reliable results can be obtained in an accelerator mass spectrometry (AMS) measurement is in many cases limited by carbon contamination introduced during sample preparation (i.e. all physical and chemical steps to which samples were subjected, starting from sampling). Efforts to reduce the sample size limit down to a few mu-g carbon require comprehensive systematic investigations to assess the amount of contamination and the process yields. We are introducing additional methods to speed up this process and to obtain more reliable results. A residual gas analyzer (RGA) is used to study combustion and graphitization reactions. We could optimize the reaction process at small CO2 pressures and identify detrimental side reactions. Knowing the composition of the residual gas in a graphitization process allows a reliable judgment on the completeness of the reaction. Further, we use isotopically enriched 13C (greater than or equal to 98% 13C) as a test material to determine contamination levels. This offers significant advantages: 1) The measurement of 12C/13C in CO2 is possible on-line with the RGA, which significantly reduces turnaround times compared to AMS measurements; 2) Both the reaction yield and the amount of contamination can be determined from a single test sample. The first applications of isotopically enriched 13C and the RGA have revealed that our prototype setup has room for improvements via better hardware; however, significant improvements of our sample processing procedures were achieved, eventually arriving at an overall contamination level of 0.12 to 0.15 mu-g C during sample preparation (i.e. freeze-drying, combustion, and graphitization) of mu-g-sized samples in aqueous solution, with above 50% yield.
  • Spatial Variation in the Marine Radiocarbon Reservoir Effect throughout the Scottish Post-Roman to Late Medieval Period: North Sea Values (500-1350 BP)

    Russell, N.; Cook, G. T.; Ascough, P. L.; Dugmore, A. J. (Department of Geosciences, The University of Arizona, 2010-01-01)
    The marine radiocarbon reservoir effect (MRE) occurs as a spatially and temporally dependent variable owing to localized changes in oceanic water composition. This study investigates Delta-R values (deviations from the global average MRE whose Delta-R = 0) during the period 500-1350 BP for the east coast of Scotland, where a complex estuarine system exists that drains into the semi-enclosed North Sea basin. Due to the availability of suitable archaeological samples, the data set has a distinct Medieval focus that spans the area from Aberdeen in the north to East Lothian in the south. Many of the Delta-R values are not significantly different from 0 (the global average), but there are occasional excursions to negative values (max -172 +/- 20) indicating the presence of younger water. These values show greater variability compared to other published data for this general region, suggesting that considerable care must be taken when dating marine derived samples from archaeological sites on the east coast of Scotland.
  • Spatial Radiocarbon and Stable Carbon Isotope Variability of Mineral and Thermal Waters in Slovakia

    Povinec, P. P.; Franko, O.; Šivo, A.; Richtáriková, M.; Breier, R.; Aggarwal, P. K.; Araguás-Araguás, L. (Department of Geosciences, The University of Arizona, 2010-01-01)
    Isotope hydrology investigations were carried out with the aim to study isotope variability in mineral and thermal waters (MTW) of Slovakia. The aquifers of MTW were formed by Triassic limestones and dolomites, which are found in the mountains as well as in the pre-Tertiary substratum of depressions and lowlands. The MTW were of artesian and/or open structures. At present, there are only boreholes available, as natural outflows have already been captured by them. Large spatial isotope variability (14C between 2 and 33.6 pMC, 18O between -11.8 and -9.8, and 13C between -12.7 and -3.4 for bicarbonates and -21 and -4.9 for free CO2) and heterogeneity of MTW was observed, indicating different origins of MTW. Corrected radiocarbon apparent ages of MTW indicate that they mostly infiltrated during the Würm and Holocene periods.
  • Spatial Distribution of ∆14C Values of Organic Matter in Surface Sediments off Saru River in Northern Japan, One Year after a Flood Event in 2006

    Nagao, Seiya; Irino, Tomohisa; Aramaki, Takafumi; Ikehara, Ken; Katayama, Hajime; Otosaka, Shigeyoshi; Uchida, Masao; Shibata, Yasuyuki (Department of Geosciences, The University of Arizona, 2010-01-01)
    Dispersion and deposition of terrestrial organic matter by flooding on the inner shelf were studied using C/N ratios, 13C, and ∆14C values of sedimentary organic matter. Surface sediment samples (top 2 cm) were collected from coastal areas near the Saru River in southwestern Hokkaido, northern Japan, 1 yr after a flood event in 2006. Riverine suspended solids were also collected at a fixed station downstream during 2006-2008. Sandy sediments were located at the front of the river mouth and the western part of the sampling area, with the 13C of organic matter ranging from -23.8 to -22.0, ∆14C of -655 to -388, and an organic carbon/total nitrogen (C/N) ratio of 5.9-7.7. On the other hand, silt and clay sediments were distributed in a restricted area 11-16 km from the river mouth, with lighter 13C (-26.7 to -24.1) and higher ∆14C (-240 to -77) of organic matter and C/N ratio (7.8-13.3). From end-member analysis, the apparently younger and less degraded organic matter in the silt and clay sediments consists mainly of terrestrial organic matter released by flood events. They remain in the depression, although most flood deposits were moved to deep-sea environments.
  • Scandinavian Models: Radiocarbon Dates and the Origin and Spreading of Passage Graves in Sweden and Denmark

    Paulsson, Bettina Schulz (Department of Geosciences, The University of Arizona, 2010-01-01)
    Approximately 2700 radiocarbon results are currently available from European megalithic contexts. The interpretation of these 14C dates is often difficult. It is not easy to connect many of them from their archaeological context to the construction or the burial phase of the graves. This paper focuses on the megaliths of Scandinavia--a special megalith region--as it is the only place in Europe with 14C dates directly referable to the construction of the passage graves, the graves have good bone preservation, and new dating sequences are available. Some 188 14C results are now available from Scandinavian passage graves. In Sweden, new data suggest that these graves were built from the first half of the 35th century BC onwards. The 14C dates from birch bark as filling material between dry walls make it possible to build a sequence for the construction phase of the passage graves in Denmark from the 33rd century BC onward. With an interpretative Bayesian statistical framework, it is possible to untangle the nuances of the differences for the origin and the spreading of the megaliths in the different regions, to define, together with the archaeological remains, possible cultural-historical processes behind these phenomena and to discuss diffusion versus convergence.
  • Simple Pretreatment Method Development for Iron and Calcium Carbonate Samples

    Park, Junghun; Hong, Wan; Choi, Han Woo; Kim, Joonkon; Kim, Gi Dong (Department of Geosciences, The University of Arizona, 2010-01-01)
    Since iron artifacts generally contain trace amounts of carbon, an iron sample needs to be relatively large, as compared to other materials, and a specially designed combustion system is required. An elemental analyzer (EA) was used for the combustion of iron without any special chemical treatment. CO2 gas with 1 mg of carbon was obtained from the combustion of an iron artifact by using an EA and reduced to graphite for accelerator mass spectrometry (AMS) measurement. In this work, AMS dating results done at the Korea Institute of Geoscience and Mineral Resources (KIGAM) for several ancient iron artifacts are presented and compared with independently estimated ages. This method was found to be useful for the pretreatment of iron artifacts that contained 0.1% carbon. A simple pretreatment method using an EA was also applied to calcium carbonate (CaCO3) samples. Samples were preheated overnight at 100-300 C, without any special chemical treatment. This removed modern CO2 contamination and the background level decreased to a comparable value measured in samples treated with phosphoric acid under vacuum.
  • Robust Bayesian Analysis, an Attempt to Improve Bayesian Sequencing

    Weninger, Franz; Steier, Peter; Kutschera, Walter; Wild, Eva Maria (Department of Geosciences, The University of Arizona, 2010-01-01)
    Bayesian sequencing of radiocarbon dates deals with the problem that in most cases there does not exist an unambiguous way to define the so-called prior function, which represents information in addition to the result of the 14C measurements alone. However, a random choice of a particular prior function can lead to biased results. In this paper, "robust Bayesian analysis," which uses a whole set of prior functions, is introduced as a more reliable method. The most important aspects of the mathematical foundation and of the practical realization of the method are described. As a general result, robust Bayesian analysis leads to higher accuracy, but paid for with reduced precision. Our investigations indicate that it seems possible to establish robust analysis for practical applications.

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