869 research outputs found

    Symbolic Formulae for Linear Mixed Models

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    A statistical model is a mathematical representation of an often simplified or idealised data-generating process. In this paper, we focus on a particular type of statistical model, called linear mixed models (LMMs), that is widely used in many disciplines e.g.~agriculture, ecology, econometrics, psychology. Mixed models, also commonly known as multi-level, nested, hierarchical or panel data models, incorporate a combination of fixed and random effects, with LMMs being a special case. The inclusion of random effects in particular gives LMMs considerable flexibility in accounting for many types of complex correlated structures often found in data. This flexibility, however, has given rise to a number of ways by which an end-user can specify the precise form of the LMM that they wish to fit in statistical software. In this paper, we review the software design for specification of the LMM (and its special case, the linear model), focusing in particular on the use of high-level symbolic model formulae and two popular but contrasting R-packages in lme4 and asreml

    A frequentist framework of inductive reasoning

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    Reacting against the limitation of statistics to decision procedures, R. A. Fisher proposed for inductive reasoning the use of the fiducial distribution, a parameter-space distribution of epistemological probability transferred directly from limiting relative frequencies rather than computed according to the Bayes update rule. The proposal is developed as follows using the confidence measure of a scalar parameter of interest. (With the restriction to one-dimensional parameter space, a confidence measure is essentially a fiducial probability distribution free of complications involving ancillary statistics.) A betting game establishes a sense in which confidence measures are the only reliable inferential probability distributions. The equality between the probabilities encoded in a confidence measure and the coverage rates of the corresponding confidence intervals ensures that the measure's rule for assigning confidence levels to hypotheses is uniquely minimax in the game. Although a confidence measure can be computed without any prior distribution, previous knowledge can be incorporated into confidence-based reasoning. To adjust a p-value or confidence interval for prior information, the confidence measure from the observed data can be combined with one or more independent confidence measures representing previous agent opinion. (The former confidence measure may correspond to a posterior distribution with frequentist matching of coverage probabilities.) The representation of subjective knowledge in terms of confidence measures rather than prior probability distributions preserves approximate frequentist validity.Comment: major revisio

    Search for CP violation in D+→ϕπ+ and D+s→K0Sπ+ decays

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    A search for CP violation in D + → ϕπ + decays is performed using data collected in 2011 by the LHCb experiment corresponding to an integrated luminosity of 1.0 fb−1 at a centre of mass energy of 7 TeV. The CP -violating asymmetry is measured to be (−0.04 ± 0.14 ± 0.14)% for candidates with K − K + mass within 20 MeV/c 2 of the ϕ meson mass. A search for a CP -violating asymmetry that varies across the ϕ mass region of the D + → K − K + π + Dalitz plot is also performed, and no evidence for CP violation is found. In addition, the CP asymmetry in the D+s→K0Sπ+ decay is measured to be (0.61 ± 0.83 ± 0.14)%

    Performance of CMS muon reconstruction in pp collision events at sqrt(s) = 7 TeV

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    The performance of muon reconstruction, identification, and triggering in CMS has been studied using 40 inverse picobarns of data collected in pp collisions at sqrt(s) = 7 TeV at the LHC in 2010. A few benchmark sets of selection criteria covering a wide range of physics analysis needs have been examined. For all considered selections, the efficiency to reconstruct and identify a muon with a transverse momentum pT larger than a few GeV is above 95% over the whole region of pseudorapidity covered by the CMS muon system, abs(eta) < 2.4, while the probability to misidentify a hadron as a muon is well below 1%. The efficiency to trigger on single muons with pT above a few GeV is higher than 90% over the full eta range, and typically substantially better. The overall momentum scale is measured to a precision of 0.2% with muons from Z decays. The transverse momentum resolution varies from 1% to 6% depending on pseudorapidity for muons with pT below 100 GeV and, using cosmic rays, it is shown to be better than 10% in the central region up to pT = 1 TeV. Observed distributions of all quantities are well reproduced by the Monte Carlo simulation.Comment: Replaced with published version. Added journal reference and DO

    Measurement of the Forward-Backward Asymmetry in the B -> K(*) mu+ mu- Decay and First Observation of the Bs -> phi mu+ mu- Decay

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    We reconstruct the rare decays B+K+μ+μB^+ \to K^+\mu^+\mu^-, B0K(892)0μ+μB^0 \to K^{*}(892)^0\mu^+\mu^-, and Bs0ϕ(1020)μ+μB^0_s \to \phi(1020)\mu^+\mu^- in a data sample corresponding to 4.4fb14.4 {\rm fb^{-1}} collected in ppˉp\bar{p} collisions at s=1.96TeV\sqrt{s}=1.96 {\rm TeV} by the CDF II detector at the Fermilab Tevatron Collider. Using 121±16121 \pm 16 B+K+μ+μB^+ \to K^+\mu^+\mu^- and 101±12101 \pm 12 B0K0μ+μB^0 \to K^{*0}\mu^+\mu^- decays we report the branching ratios. In addition, we report the measurement of the differential branching ratio and the muon forward-backward asymmetry in the B+B^+ and B0B^0 decay modes, and the K0K^{*0} longitudinal polarization in the B0B^0 decay mode with respect to the squared dimuon mass. These are consistent with the theoretical prediction from the standard model, and most recent determinations from other experiments and of comparable accuracy. We also report the first observation of the Bs0ϕμ+μdecayandmeasureitsbranchingratioB^0_s \to \phi\mu^+\mu^- decay and measure its branching ratio {\mathcal{B}}(B^0_s \to \phi\mu^+\mu^-) = [1.44 \pm 0.33 \pm 0.46] \times 10^{-6}using using 27 \pm 6signalevents.Thisiscurrentlythemostrare signal events. This is currently the most rare B^0_s$ decay observed.Comment: 7 pages, 2 figures, 3 tables. Submitted to Phys. Rev. Let

    Performance of CMS muon reconstruction in pp collision events at sqrt(s) = 7 TeV

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    The performance of muon reconstruction, identification, and triggering in CMS has been studied using 40 inverse picobarns of data collected in pp collisions at sqrt(s) = 7 TeV at the LHC in 2010. A few benchmark sets of selection criteria covering a wide range of physics analysis needs have been examined. For all considered selections, the efficiency to reconstruct and identify a muon with a transverse momentum pT larger than a few GeV is above 95% over the whole region of pseudorapidity covered by the CMS muon system, abs(eta) < 2.4, while the probability to misidentify a hadron as a muon is well below 1%. The efficiency to trigger on single muons with pT above a few GeV is higher than 90% over the full eta range, and typically substantially better. The overall momentum scale is measured to a precision of 0.2% with muons from Z decays. The transverse momentum resolution varies from 1% to 6% depending on pseudorapidity for muons with pT below 100 GeV and, using cosmic rays, it is shown to be better than 10% in the central region up to pT = 1 TeV. Observed distributions of all quantities are well reproduced by the Monte Carlo simulation.Comment: Replaced with published version. Added journal reference and DO

    Search for the standard model Higgs boson at LEP

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    Measurements of the properties of Lambda_c(2595), Lambda_c(2625), Sigma_c(2455), and Sigma_c(2520) baryons

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    We report measurements of the resonance properties of Lambda_c(2595)+ and Lambda_c(2625)+ baryons in their decays to Lambda_c+ pi+ pi- as well as Sigma_c(2455)++,0 and Sigma_c(2520)++,0 baryons in their decays to Lambda_c+ pi+/- final states. These measurements are performed using data corresponding to 5.2/fb of integrated luminosity from ppbar collisions at sqrt(s) = 1.96 TeV, collected with the CDF II detector at the Fermilab Tevatron. Exploiting the largest available charmed baryon sample, we measure masses and decay widths with uncertainties comparable to the world averages for Sigma_c states, and significantly smaller uncertainties than the world averages for excited Lambda_c+ states.Comment: added one reference and one table, changed order of figures, 17 pages, 15 figure
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