Summed Probability Distributions Research Articles

Regional variation in the terminal Pleistocene and early Holocene radiocarbon record of eastern North America

In this paper we use radiocarbon dates to evaluate the signature of the Younger Dryas Chronozone (YDC) in eastern North America. Using an approach that examines radiocarbon dates by region, we argue that the northeastern United States shows a better overall representation of radiocarbon dates when compared to the Mid-Atlantic and Southeast. These data result in a peak in summed probability distributions during the YDC, which is often interpreted as evidence of population growth. Further examination of these distributions, however, illustrates that differential standard deviations, varying sample size, and the effect of taphonomic and research biases likely overwhelm any demographic signatures in our study sample. Consequently, the frequency of radiocarbon dates by itself is insufficient for understanding the relationship between climate, culture and demography in eastern North America.

Bounds for the approximation of Poisson-binomial distribution by Poisson distribution

Let ( , ; ) be a row-wise triangular array of independent Bernoulli random variables with success probabilities , ; . For every , the random variables have probability distributions with complicated structure and therefore they are used to being approximated by Poisson distribution. Well-known Le Cam’s inequality is established for providing information on the quality of a Poisson approximation. The main aim of this paper is to re-establish the Le Cam-type inequalities via a linear operator. The operator method used in this paper is quite elementary and it also could be applied for the probability distributions of random sums in the Poisson approximation, where , , are positive integer-valued random variables, independent of all , ; . MSC:60F05, 60G50, 41A36.

Generalized Huberman-Rudnick scaling law and robustness of q-Gaussian probability distributions

We generalize Huberman-Rudnick universal scaling law for all periodic windows of the logistic map and show the robustness of q-Gaussian probability distributions in the vicinity of chaos threshold. Our scaling relation is universal for the self-similar windows of the map which exhibit period-doubling subharmonic bifurcations. Using this generalized scaling argument, for all periodic windows, as chaos threshold is approached, a developing convergence to q-Gaussian is numerically obtained both in the central regions and tails of the probability distributions of sums of iterates.

Temporal Dynamics of East Texas Caddo Sites with 10 or More Radiocarbon Dates

This article represents supplementary data highlighting the specifics of date combination and the subsequent production of summed probability distribution samples for Caddo sites in East Texas. All radiocarbon (14C) dates employed in this effort were collected from research and cultural resource management (CRM) reports and publications, synthesized, then recalibrated in version 4.1.7 of OxCal using IntCal09. The raw sample of Caddo 14C dates (n=889, with a standard deviation of 58) exceeds the minimum number of dates-750 suggested by Michczynska and Pazdur and 500 by Williams - but the combined sample (n=407, with a standard deviation of 53) does not meet the required minimum number of dates necessary to achieve significance. However, the distilled sample of 407 dates reduces probability bias introduced by sites with large numbers of 14C dates, and provides a more accurate representation of the temporal character for sites with ~10 14C dates.

A Preliminary Temporal Analysis of the East Texas Archaic

This article presents preliminary findings of a temporal analysis of the East Texas Archaic based upon the examination of radiocarbon 14C dates from sites that have deposits that date to the period. All assays employed in this effort were collected from research and cultural resource management reports and publications, synthesized, then recalibrated in version 4.1.7 of OxCal using IntCal09. The date combination process is used herein to refine site-specific summed probability distributions, illustrating— for the first time—the temporal position of each dated archaeological site with an assay that falls within the Archaic. Seventy-three radiocarbon dates from 34 sites serve as the foundation for this analysis of the East Texas Archaic period (ca. 8000-500 B.C.) (Table 1). All dates used in this analysis come directly from the East Texas Radiocarbon Database (ETRD). Within the sample, there are 19 sites with a single radiocarbon sample that dates to the Archaic, eight sites with two dated samples, one site with three dated samples, three sites with four dated samples, one site with five dated samples, and one site with 14 dated samples. Of the 73 14C dates from the ETRD used in this analysis, one dates to the Early Archaic period (ca. 8000-5000 B.C.), eight date to the Middle Archaic period (ca. 5000-3000 B.C.), and the remaining 64 date to the Late Archaic period (ca. 3000-500 B.C.) (temporal divisions follow Perttula and Young).

Impact of the spatial congruence of redundant targets on within-modal and cross-modal integration

Although the topic of sensory integration has raised increasing interest, the differing behavioral outcome of combining unisensory versus multisensory inputs has surprisingly only been scarcely investigated. In the present experiment, observers were required to respond as fast as possible to (1) lateralized visual or tactile targets presented alone, (2) double stimulation within the same modality or (3) double stimulation across modalities. Each combination was either delivered within the same hemispace (spatially aligned) or in different hemispaces (spatially misaligned). Results show that the redundancy gains (RG) obtained from the cross-modal conditions were far greater than those obtained from combinations of two visual or two tactile targets. Consistently, we observed that the reaction time distributions of cross-modal targets, but not those of within-modal targets, surpass the predicted reaction time distribution based on the summed probability distributions of each constituent stimulus presented alone. Moreover, we found that the spatial alignment of the targets did not influence the RG obtained in cross-modal conditions, whereas within-modal stimuli produced a greater RG when the targets where delivered in separate hemispaces. These results suggest that within-modal and cross-modal integration are not only distinguishable by the amount of facilitation they produce, but also by the spatial configuration under which this facilitation occurs. Our study strongly supports the notion that estimates of the same event that are more independent produce enhanced integrative gains.

Radiocarbon calibration curves, summed probability distributions, and early Paleoindian population trends in North America

Archaeologists increasingly examine summed probability distributions of radiocarbon dates to search for temporal trends in ancient human populations, including early North American population trends across the onset of the Younger Dryas climatic period (10,900 BC). We use both IntCal04 and IntCal09 to simulate and calibrate sequences of radiocarbon dates that represent evenly spaced calendar ages from 12,000 to 9000 BC and use IntCal09 to simulate two different demographic processes across this interval. The shapes of the calibrated summed probability distribution from our first set of simulations mirror many trends that have been interpreted in demographic terms and this shape shows clear links to the shape of the radiocarbon calibration curve. This is true for both IntCal04 and IntCal09, although these different curves produce different probability distributions. The shapes of the calibrated summed probability distribution from our second set of simulations differ somewhat but show virtually identical trends at points where the actual frequencies of calendar dates are very different. We conclude that changing frequencies of radiocarbon dates over time probably do contain demographic information, but that extracting this information is more difficult than archaeologists have acknowledged.

Modeling Regional Radiocarbon Trends: A Case Study from the East Texas Woodland Period

The East Texas Radiocarbon Database contributes to an analysis of tempo and place for Woodland era (∼500 BC–AD 800) archaeological sites within the region. The temporal and spatial distributions of calibrated14C ages (n= 127) with a standard deviation (ΔT) of 61 from archaeological sites with Woodland components (n= 51) are useful in exploring the development and geographical continuity of the peoples in cast Texas, and lead to a refinement of our current chronological understanding of the period. While analysis of summed probability distributions (SPDs) produces less than significant findings due to sample size, they are used here to illustrate the method of date combination prior to the production of site- and period-specific SPDs. Through the incorporation of this method, the number of14C dates is reduced to 85 with a ΔTof 54. The resultant data set is then subjected to statistical analyses that conclude with the separation of the east Texas Woodland period into the Early Woodland (∼500 BC–AD 0), Middle Woodland (∼AD 0–400), and Late Woodland (∼AD 400–800) periods.

Modeling Regional Radiocarbon Trends: A Case Study from the East Texas Woodland Period

The East Texas Radiocarbon Database contributes to an analysis of tempo and place for Woodland era (∼500 BC–AD 800) archaeological sites within the region. The temporal and spatial distributions of calibrated 14C ages (n = 127) with a standard deviation (ΔT) of 61 from archaeological sites with Woodland components (n = 51) are useful in exploring the development and geographical continuity of the peoples in cast Texas, and lead to a refinement of our current chronological understanding of the period. While analysis of summed probability distributions (SPDs) produces less than significant findings due to sample size, they are used here to illustrate the method of date combination prior to the production of site- and period-specific SPDs. Through the incorporation of this method, the number of 14C dates is reduced to 85 with a ΔT of 54. The resultant data set is then subjected to statistical analyses that conclude with the separation of the east Texas Woodland period into the Early Woodland (∼500 BC–AD 0), Middle Woodland (∼AD 0–400), and Late Woodland (∼AD 400–800) periods.

Did the mid-Holocene environmental changes cause the boom and bust of hunter-gatherer population size in eastern Fennoscandia?

Prehistoric hunter-gatherer population size is often assumed to follow climatic and other environmental forcings that affect environmental productivity and the availability of food for human foragers. We tested this assumption by studying the co-variation of archaeological and palaeoenvironmental records during the Holocene in eastern Fennoscandia. The reconstruction of population history is based on the summed probability distribution of archaeological radiocarbon dates, and environmental changes are tracked with locally available, high-resolution biological and physical proxies that are relevant in terms of hunter-gatherer food availability and population dynamics. The results show major population growth during the period of high summer temperature and high productivity of the terrestrial, lacustrine and marine ecosystems that occurred during 7500–5700 cal. yr BP. The growth was followed by an abrupt decline during 5500–4000 cal. yr BP correlating with the onset of late-Holocene cooling and a major forest ecosystem change brought about by the expansion of Norway spruce and the associated change from species-rich mixed forests to a conifer-dominated boreal ecosystem. Forest ecosystem changes likely enforced the negative effects of decreasing productivity on hunter-gatherer food availability. The link between population and environmental proxies breaks down along with the intensification of agriculture after 3500 cal. yr BP, which indicates that agriculture weakened the environmental forcing on long-term human population dynamics.

A comment on Steele’s (2010) “radiocarbon dates as data: quantitative strategies for estimating colonization front speeds and event densities”

We show that Steele’s (2010) criticisms of Hamilton and Buchanan (2007) and Buchanan et al. (2008) do not hold water and demonstrate that his re-analyses of Hamilton and Buchanan’s (2007) and Buchanan et al'.s (2008) datasets are flawed. In the process, we highlight some important issues for researchers interested in using radiocarbon dates to reconstruct population movements and demography. Most notably, we explain why OLS regression is preferable to RMA regression when estimating diffusion velocity, and demonstrate that the summed probability distributions yielded by CalPal are more reliable as guides to past demographic change than those produced by Calib and OxCal.

Northern peatland initiation lagged abrupt increases in deglacial atmospheric CH 4

Peatlands are a key component of the global carbon cycle. Chronologies of peatland initiation are typically based on compiled basal peat radiocarbon (14C) dates and frequency histograms of binned calibrated age ranges. However, such compilations are problematic because poor quality 14C dates are commonly included and because frequency histograms of binned age ranges introduce chronological artefacts that bias the record of peatland initiation. Using a published compilation of 274 basal 14C dates from Alaska as a case study, we show that nearly half the 14C dates are inappropriate for reconstructing peatland initiation, and that the temporal structure of peatland initiation is sensitive to sampling biases and treatment of calibrated 14C dates. We present revised chronologies of peatland initiation for Alaska and the circumpolar Arctic based on summed probability distributions of calibrated 14C dates. These revised chronologies reveal that northern peatland initiation lagged abrupt increases in atmospheric CH4 concentration at the start of the Bølling-Allerød interstadial (Termination 1A) and the end of the Younger Dryas chronozone (Termination 1B), suggesting that northern peatlands were not the primary drivers of the rapid increases in atmospheric CH4. Our results demonstrate that subtle methodological changes in the synthesis of basal 14C ages lead to substantially different interpretations of temporal trends in peatland initiation, with direct implications for the role of peatlands in the global carbon cycle.

Reduced multisensory integration in patients with schizophrenia on a target detection task

A growing body of literature demonstrates impaired multisensory integration (MSI) in patients with schizophrenia compared to non-psychiatric individuals. One of the most basic measures of MSI is intersensory facilitation of reaction times (RTs), in which bimodal targets, with cues from two sensory modalities, are detected faster than unimodal targets. This RT speeding is generally attributed to super-additive processing of multisensory targets. In order to test whether patients with schizophrenia are impaired on this basic measure of MSI, we assessed the degree of intersensory facilitation for a sample of 20 patients compared to 20 non-psychiatric individuals using a very simple target detection task. RTs were recorded for participants to detect targets that were either unimodal (auditory alone, A; visual alone, V) or bimodal (auditory+visual, AV). RT distributions to detect bimodal targets were compared with predicted RT distributions based on the summed probability distribution of each participant's RTs to visual alone and auditory alone targets. Patients with schizophrenia showed less RT facilitation when detecting bimodal targets relative to non-psychiatric individuals, even when groups were matched for unimodal RTs. Within the schizophrenia group, RT benefit was correlated with negative symptoms, such that patients with greater negative symptoms showed the least RT facilitation (r2=0.20, p<0.05). Additionally, schizophrenia patients who experienced both auditory and visual hallucinations showed less multisensory benefit compared to patients who experienced only auditory hallucinations, indicating that the presence of hallucinations in two modalities may more strongly impair MSI compared to hallucinations in only one modality.

Asymptotic expansions of probability distributions

Asymtotic expansionsfor the probabilitydistributionsof sums of independentrandom variables are studied in this paper.

Prehistoric population history in eastern Fennoscandia

In this article, prehistoric population history in eastern Fennoscandia is modelled using summed probability distributions of radiocarbon dates. In addition, radiocarbon date distribution is compared with other proxy data. Different proxies seem to produce similar distributions, which enhances the overall reliability of the pattern. The results indicate that there was a very pronounced peak in the hunter–gatherer population slightly after 4000 cal BC. This peak seems to be linked to increased environmental productivity. The subsequent population decline culminated just before the local appearance of farming economies in different sub-areas, which is an interesting result in the wider northern and central European context. Along with the adoption of agriculture, new population growth began in eastern Fennoscandia.

Optically stimulated luminescence dating of young (

The reliability of single-grain optically stimulated luminescence (OSL) dating of young (<500 years old) samples is assessed by examining the results of 166 single-grain OSL analyses of Australian alluvial, lacustrine, estuarine, coastal and marine sediment samples. All samples have been analysed using the modified SAR protocol of Olley et al. [2004b. Optical dating of Holocene sediments from a variety of geomorphic settings using single grains of quartz. Geomorphology 60, 337–358], with burial doses ( D b) calculated by fitting a single Gaussian curve to the peak of a multi-Gaussian summed probability distribution (PDF Gaussian). The near-equivalence of this approach to currently accepted methods of palaeodose estimation – namely the minimum age and central age models of Galbraith et al. [1999. Optical dating of single and multiple grains of quartz from Jinmium rock shelter, northern Australia: part I, experimental design and statistical models. Archaeometry 41, 339–364] – is demonstrated. Considered as a whole, OSL ages calculated using the PDF Gaussian D b determination method are consistent with other chronometric, geomorphological, botanical and historical indicators of depositional age, while four alternative (previously published) methods are generally less reliable when applied to the samples analysed here. The single-grain data from 12 samples of known age (reported by Olley et al. [2004b. Optical dating of Holocene sediments from a variety of geomorphic settings using single grains of quartz. Geomorphology 60, 337–358]) are re-analysed using the PDF Gaussian approach, with all but one yielding a D b consistent with the independently known age. Examples of luminescence data (dose recovery tests, preheat plateaux, continuous-wave and linear-modulated OSL, growth curves, single-grain dose distributions) are provided that together indicate the suitability of Australian quartz for dating young sediments.

Closer look at time averages of the logistic map at the edge of chaos

The probability distribution of sums of iterates of the logistic map at the edge of chaos has been recently shown [U. Tirnakli, Phys. Rev. E 75, 040106(R) (2007)] to be numerically consistent with a q-Gaussian, the distribution which-under appropriate constraints-maximizes the nonadditive entropy Sq, which is the basis of nonextensive statistical mechanics. This analysis was based on a study of the tails of the distribution. We now check the entire distribution, in particular, its central part. This is important in view of a recent q generalization of the central limit theorem, which states that for certain classes of strongly correlated random variables the rescaled sum approaches a q-Gaussian limit distribution. We numerically investigate for the logistic map with a parameter in a small vicinity of the critical point under which conditions there is convergence to a q-Gaussian both in the central region and in the tail region and find a scaling law involving the Feigenbaum constant delta. Our results are consistent with a large number of already available analytical and numerical evidences that the edge of chaos is well described in terms of the entropy Sq and its associated concepts.

Analysis of samples from finite population

This paper deals with asymptotic properties of probabilitydistributionsof sample statistics when samples are selected from finite populations.These properties also were analysed by P. Erdos, A. Rényi [3] and J. Hájek [4]. Relationships between probability distributions of sample sums were investigated in [6] article.

Paleoindian demography and the extraterrestrial impact hypothesis

Recently it has been suggested that one or more large extraterrestrial (ET) objects struck northern North America 12,900 +/- 100 calendar years before present (calBP) [Firestone RB, et al. (2007) Proc Natl Acad Sci USA 104: 16016-16021]. This impact is claimed to have triggered the Younger Dryas major cooling event and resulted in the extinction of the North American megafauna. The impact is also claimed to have caused major cultural changes and population decline among the Paleoindians. Here, we report a study in which approximately 1,500 radiocarbon dates from archaeological sites in Canada and the United States were used to test the hypothesis that the ET resulted in population decline among the Paleoindians. Following recent studies [e.g., Gamble C, Davies W, Pettitt P, Hazelwood L, Richards M (2005) Camb Archaeol J 15:193-223), the summed probability distribution of the calibrated dates was used to identify probable changes in human population size between 15,000 and 9,000 calBP. Subsequently, potential biases were evaluated by modeling and spatial analysis of the dated occupations. The results of the analyses were not consistent with the predictions of extraterrestrial impact hypothesis. No evidence of a population decline among the Paleoindians at 12,900 +/- 100 calBP was found. Thus, minimally, the study suggests the extraterrestrial impact hypothesis should be amended.

Finding efficient recursions for risk aggregation by computer algebra

We derive recursions for the probability distribution of random sums by computer algebra. Unlike the well-known Panjer-type recursions, they are of finite order and thus allow for computation in linear time. This efficiency is bought by the assumption that the probability generating function of the claim size be algebraic. The probability generating function of the claim number is supposed to be from the rather general class of D -finite functions.