Bayesian Approach to Spectral Function Reconstruction for Euclidean Quantum Field Theories

We present a novel approach to the inference of spectral functions from Euclidean time correlator data that makes close contact with modern Bayesian concepts. Our method differs significantly from the maximum entropy method (MEM). A new set of axioms is postulated for the prior probability, leading to an improved expression, which is devoid of the asymptotically flat directions present in the Shanon-Jaynes entropy. Hyperparameters are integrated out explicitly, liberating us from the Gaussian approximations underlying the evidence approach of the maximum entropy method. We present a realistic test of our method in the context of the nonperturbative extraction of the heavy quark potential. Based on hard-thermal-loop correlator mock data, we establish firm requirements in the number of data points and their accuracy for a successful extraction of the potential from lattice QCD. Finally we reinvestigate quenched lattice QCD correlators from a previous study and provide an improved potential estimation at T2.33TC.

A new Bayesian approach to the reconstruction of spectral functions

We present a novel approach for the reconstruction of spectra from Euclidean correlator data that makes close contact to modern Bayesian concepts. It is based upon an axiomatically justified dimensionless prior distribution, which in the case of constant prior function m(ω) only imprints smoothness on the reconstructed spectrum. In addition we are able to analytically integrate out the only relevant overall hyper-parameter α in the prior, removing the necessity for Gaussian approximations found e.g. in the Maximum Entropy Method. Using a quasi-Newton minimizer and high-precision arithmetic, we are then able to find the unique global extremum of P[ρ|D] in the full Nω » Nτ dimensional search space. The method actually yields gradually improving reconstruction results if the quality of the supplied input data increases, without introducing artificial peak structures, often encountered in the MEM. To support these statements we present mock data analyses for the case of zero width delta peaks and more realistic scenarios, based on the perturbative Euclidean Wilson Loop as well as the Wilson Line correlator in Coulomb gauge.

Bayesian statistics in oncology: a guide for the clinical investigator

The rise of evidence-based medicine as well as important progress in statistical methods and computational power have led to a second birth of the >200-year-old Bayesian framework. The use of Bayesian techniques, in particular in the design and interpretation of clinical trials, offers several substantial advantages over the classical statistical approach. First, in contrast to classical statistics, Bayesian analysis allows a direct statement regarding the probability that a treatment was beneficial. Second, Bayesian statistics allow the researcher to incorporate any prior information in the analysis of the experimental results. Third, Bayesian methods can efficiently handle complex statistical models, which are suited for advanced clinical trial designs. Finally, Bayesian statistics encourage a thorough consideration and presentation of the assumptions underlying an analysis, which enables the reader to fully appraise the authors' conclusions. Both Bayesian and classical statistics have their respective strengths and limitations and should be viewed as being complementary to each other; we do not attempt to make a head-to-head comparison, as this is beyond the scope of the present review. Rather, the objective of the present article is to provide a nonmathematical, reader-friendly overview of the current practice of Bayesian statistics coupled with numerous intuitive examples from the field of oncology. It is hoped that this educational review will be a useful resource to the oncologist and result in a better understanding of the scope, strengths, and limitations of the Bayesian approach.

An urn-based Bayesian block bootstrap

Block bootstrap has been introduced in the literature for resampling dependent data, i.e. stationary processes. One of the main assumptions in block bootstrapping is that the blocks of observations are exchangeable, i.e. their joint distribution is immune to permutations. In this paper we propose a new Bayesian approach to block bootstrapping, starting from the construction of exchangeable blocks. Our sampling mechanism is based on a particular class of reinforced urn processes

Benchmarking the Bayesian reconstruction of the non-perturbative heavy ǪǬ potential

The extraction of the finite temperature heavy quark potential from lattice QCD relies on a spectral analysis of the real-time Wilson loop. Through its position and shape, the lowest lying spectral peak encodes the real and imaginary part of this complex potential. We benchmark this extraction strategy using leading order hard-thermal loop (HTL) calculations. I.e. we analytically calculate the Wilson loop and determine the corresponding spectrum. By fitting its lowest lying peak we obtain the real- and imaginary part and confirm that the knowledge of the lowest peak alone is sufficient for obtaining the potential. We deploy a novel Bayesian approach to the reconstruction of spectral functions to HTL correlators in Euclidean time and observe how well the known spectral function and values for the real and imaginary part are reproduced. Finally we apply the method to quenched lattice QCD data and perform an improved estimate of both real and imaginary part of the non-perturbative heavy ǪǬ potential.

Genetic diversity among horse populations with a special focus on the Franches-Montagnes breed

Genetic characterization helps to assure breed integrity and to assign individuals to defined populations. The objective of this study was to characterize genetic diversity in six horse breeds and to analyse the population structure of the Franches-Montagnes breed, especially with regard to the degree of introgression with Warmblood. A total of 402 alleles from 50 microsatellite loci were used. The average number of alleles per locus was significantly lower in Thoroughbreds and Arabians. Average heterozygosities between breeds ranged from 0.61 to 0.72. The overall average of the coefficient of gene differentiation because of breed differences was 0.100, with a range of 0.036-0.263. No significant correlation was found between this parameter and the number of alleles per locus. An increase in the number of homozygous loci with increasing inbreeding could not be shown for the Franches-Montagnes horses. The proportion of shared alleles, combined with the neighbour-joining method, defined clusters for Icelandic Horse, Comtois, Arabians and Franches-Montagnes. A more disparate clustering could be seen for European Warmbloods and Thoroughbreds, presumably from frequent grading-up of Warmbloods with Thoroughbreds. Grading-up effects were also observed when Bayesian and Monte Carlo resampling approaches were used for individual assignment to a given population. Individual breed assignments to defined reference populations will be very difficult when introgression has occurred. The Bayesian approach within the Franches-Montagnes breed differentiated individuals with varied proportions of Warmblood.

HHV-8 seroprevalence: a global view

BACKGROUND Human herpes virus 8 (HHV-8) is the underlying infectious cause of Kaposi sarcoma (KS) and other proliferative diseases; that is, primary effusion lymphoma and multicentric Castleman disease. In regions with high HHV-8 seroprevalence in the general population, KS accounts for a major burden of disease. Outside these endemic regions, HHV-8 prevalence is high in men who have sex with men (MSM) and in migrants from endemic regions. We aim to conduct a systematic literature review and meta-analysis in order 1) to define the global distribution of HHV-8 seroprevalence (primary objective) and 2) to identify risk factors for HHV-8 infection, with a focus on HIV status (secondary objective). METHODS/DESIGN We will include observational studies reporting data on seroprevalence of HHV-8 in children and/or adults from any region in the world. Case reports and case series as well as any studies with fewer than 50 participants will be excluded. We will search MEDLINE, EMBASE, and relevant conference proceedings without language restriction. Two reviewers will independently screen the identified studies and extract data on study characteristics and quality, study population, risk factors, and reported outcomes, using a standardized form. For the primary objective we will pool the data using a fully bayesian approach for meta-analysis, with random effects at the study level. For the secondary objective (association of HIV and HHV-8) we aim to pool odds ratios for the association of HIV and HHV-8 using a fully bayesian approach for meta-analysis, with random effects at the study level. Sub-group analyses and meta-regression analyses will be used to explore sources of heterogeneity, including factors such as geographical region, calendar years of recruitment, age, gender, ethnicity, socioeconomic status, different risk groups for sexually and parenterally transmitted infections (MSM, sex workers, hemophiliacs, intravenous drug users), comorbidities such as organ transplantation and malaria, test(s) used to measure HHV-8 infection, study design, and study quality. DISCUSSION Using the proposed systematic review and meta-analysis, we aim to better define the global seroprevalence of HHV-8 and its associated risk factors. This will improve the current understanding of HHV-8 epidemiology, and could suggest measures to prevent HHV-8 infection and to reduce its associated cancer burden.

Allowable carbon emissions lowered by multiple climate targets

Climate targets are designed to inform policies that would limit the magnitude and impacts of climate change caused by anthropogenic emissions of greenhouse gases and other substances. The target that is currently recognized by most world governments1 places a limit of two degrees Celsius on the global mean warming since preindustrial times. This would require large sustained reductions in carbon dioxide emissions during the twenty-first century and beyond2, 3, 4. Such a global temperature target, however, is not sufficient to control many other quantities, such as transient sea level rise5, ocean acidification6, 7 and net primary production on land8, 9. Here, using an Earth system model of intermediate complexity (EMIC) in an observation-informed Bayesian approach, we show that allowable carbon emissions are substantially reduced when multiple climate targets are set. We take into account uncertainties in physical and carbon cycle model parameters, radiative efficiencies10, climate sensitivity11 and carbon cycle feedbacks12, 13 along with a large set of observational constraints. Within this framework, we explore a broad range of economically feasible greenhouse gas scenarios from the integrated assessment community14, 15, 16, 17 to determine the likelihood of meeting a combination of specific global and regional targets under various assumptions. For any given likelihood of meeting a set of such targets, the allowable cumulative emissions are greatly reduced from those inferred from the temperature target alone. Therefore, temperature targets alone are unable to comprehensively limit the risks from anthropogenic emissions.

The dating of dipterocarp tree rings: establishing a record of carbon cycling and climatic change in the tropics

In a first step to obtain a proxy record of past climatic events (including the El Ni (n) over tildeo-Southern Oscillation) in the normally aseasonal tropical environment of Sabah, a radial segment from a recently fallen dipterocarp (Shorea Superba) was radiocarbon dated and subjected to carbon isotope analysis. The high-precision radiocarbon results fell into the ambiguous modern plateau where several calibrated dates can exist for each sample. Dating was achieved by wiggle matching using a Bayesian approach to calibration. Using the defined growth characteristics of Shorea superba, probability density distributions were calculated and improbable dates rejected. It was found that the tree most likely started growing around AD 1660-1685. A total of 173 apparent growth increments were measured and, therefore, it could be determined that the tree formed one ring approximately every two years. Stable carbon isotope values were obtained from resin-extracted wholewood from each ring. Carbon cycling is evident in the `juvenile effect', resulting from the assimilation of respired carbon dioxide and lower light levels below the canopy, and in the `anthropogenic effect' caused by increased industrial activity in the late-nineteenth and twentieth centuries. This study demonstrates that palaeoenvironmental information can be obtained from trees growing in aseasonal environments, where climatic conditions prevent the formation of well-defined annual rings.

Search for contact interactions and large extra dimensions in dilepton events from pp collisions at sqrts=7 TeV with the ATLAS detector

A search for nonresonant new phenomena, originating from either contact interactions or large extra spatial dimensions, has been carried out using events with two isolated electrons or muons. These events, produced at the LHC in proton-proton collisions at root s = 7 TeV, were recorded by the ATLAS detector. The data sample, collected throughout 2011, corresponds to an integrated luminosity of 4.9 and 5.0 fb(-1) in the e(+)e(-) and mu(+)mu(-) channels, respectively. No significant deviations from the Standard Model expectation are observed. Using a Bayesian approach, 95% confidence level lower limits ranging from 9.0 to 13.9 TeV are placed on the energy scale of llqq contact interactions in the left-left isoscalar model. Lower limits ranging from 2.4 to 3.9 TeV are also set on the string scale in large extra dimension models. After combining these limits with results from a similar search in the diphoton channel, slightly more stringent limits are obtained.

Using Bayes' rule to define the value of evidence from syndromic surveillance

In this work we propose the adoption of a statistical framework used in the evaluation of forensic evidence as a tool for evaluating and presenting circumstantial "evidence" of a disease outbreak from syndromic surveillance. The basic idea is to exploit the predicted distributions of reported cases to calculate the ratio of the likelihood of observing n cases given an ongoing outbreak over the likelihood of observing n cases given no outbreak. The likelihood ratio defines the Value of Evidence (V). Using Bayes' rule, the prior odds for an ongoing outbreak are multiplied by V to obtain the posterior odds. This approach was applied to time series on the number of horses showing clinical respiratory symptoms or neurological symptoms. The separation between prior beliefs about the probability of an outbreak and the strength of evidence from syndromic surveillance offers a transparent reasoning process suitable for supporting decision makers. The value of evidence can be translated into a verbal statement, as often done in forensics or used for the production of risk maps. Furthermore, a Bayesian approach offers seamless integration of data from syndromic surveillance with results from predictive modeling and with information from other sources such as disease introduction risk assessments.