Approximate Inference for Robust Gaussian Process Regression

Gaussian process (GP) priors have been successfully used in non-parametric Bayesian regression and classification models. Inference can be performed analytically only for the regression model with Gaussian noise. For all other likelihood models inference is intractable and various approximation techniques have been proposed. In recent years expectation-propagation (EP) has been developed as a general method for approximate inference. This article provides a general summary of how expectation-propagation can be used for approximate inference in Gaussian process models. Furthermore we present a case study describing its implementation for a new robust variant of Gaussian process regression. To gain further insights into the quality of the EP approximation we present experiments in which we compare to results obtained by Markov chain Monte Carlo (MCMC) sampling

High p_T Spectra of Identified Particles Produced in Pb+Pb Collisions at 158GeV/nucleon Beam Energy

Transverse momentum spectra of pi^{+/-}, p, pbar, K^{+/-}, K^0_s and Lambda at midrapidity were measured at high p_T in Pb+Pb collisions at 158GeV/nucleon beam energy by the NA49 experiment. Particle yield ratios (p/pi, K/pi and Lambda/K^0_s) show an enhancement of the baryon/meson ratio for p_T>2GeV/c. The nuclear modification factor R_{CP} is extracted and compared to RHIC measurements and pQCD calculations.Comment: Quark Matter 2005 parallel section proceeding

Baryon Stopping and Charged Particle Distributions in Central Pb+Pb Collisions at 158 GeV per Nucleon

Net proton and negative hadron spectra for central \PbPb collisions at 158 GeV per nucleon at the CERN SPS were measured and compared to spectra from lighter systems. Net baryon distributions were derived from those of net protons, utilizing model calculations of isospin contributions as well as data and model calculations of strange baryon distributions. Stopping (rapidity shift with respect to the beam) and mean transverse momentum \meanpt of net baryons increase with system size. The rapidity density of negative hadrons scales with the number of participant nucleons for nuclear collisions, whereas their \meanpt is independent of system size. The \meanpt dependence upon particle mass and system size is consistent with larger transverse flow velocity at midrapidity for \PbPb compared to \SS central collisions.Comment: This version accepted for publication in PRL. 4 pages, 3 figures. Typos corrected, some paragraphs expanded in response to referee comments, to better explain details of analysi

Multiplicity fluctuations in nuclear collisions at 158 A GeV

System size dependence of multiplicity fluctuations of charged particles produced in nuclear collisions at 158 A GeV was studied in the NA49 CERN experiment. Results indicate a non-monotonic dependence of the scaled variance of the multiplicity distribution with a maximum for semi-peripheral Pb+Pb interactions with number of projectile participants of about 35. This effect is not observed in a string-hadronic model of nuclear collision HIJING.Comment: Presented at "Focus on Multiplicity", 17-19 of June, Bari, Ital

High p_T Spectra of Identified Particles Produced in Pb+Pb Collisions at 158A GeV Beam Energy

Results of the NA49 collaboration on the production of hadrons with large transverse momentum in Pb+Pb collisions at 158A GeV beam energy are presented. A range up to p_T = 4 GeV/c is covered. The nuclear modification factor R_CP is extracted for pions, kaons and protons, and the baryon to meson ratios p/pi+, pbar/pi- and Lambda/K^0_s are studied. All results are compared to other measurements at SPS and RHIC and to theoretical calculations.Comment: Submitted to J. Phys. G (Proceedings of the 9th International Conference on Strangeness in Quark Matter, Los Angeles, USA, March 26-31, 2006). 5 pages, 3 figure

Strangeness production at SPS energies

We present a summary of measurements of strange particles performed by the experiment NA49 in central and minimum bias Pb+Pb collisions in the beam energy range 20A - 158A GeV. New results on Xi production in central Pb+Pb collisions and on Lambda, Xi production in minimum bias collisions are shown. Transverse mass spectra and rapidity distributions of strange particles at different energies are compared. The energy dependence of the particle yields and ratios is discussed. NA49 measurements of the Lambda and Xi enhancement factors are shown for the first time.Comment: Submitted to J. Phys. G (Proceedings of the 9th International Conference on Strangeness in Quark Matter, Los Angeles, USA, March 26-31, 2006). 9 pages, 9 figure

Event-by-event fluctuations of average transverse momentum in central Pb+Pb collisions at 158 GeV per nucleon

We present first data on event-by-event fluctuations in the average transverse momentum of charged particles produced in Pb+Pb collisions at the CERN SPS. This measurement provides previously unavailable information allowing sensitive tests of microscopic and thermodynamic collision models and to search for fluctuations expected to occur in the vicinity of the predicted QCD phase transition. We find that the observed variance of the event-by-event average transverse momentum is consistent with independent particle production modified by the known two-particle correlations due to quantum statistics and final state interactions and folded with the resolution of the NA49 apparatus. For two specific models of non-statistical fluctuations in transverse momentum limits are derived in terms of fluctuation amplitude. We show that a significant part of the parameter space for a model of isospin fluctuations predicted as a consequence of chiral symmetry restoration in a non-equilibrium scenario is excluded by our measurement.Comment: 6 pages, 2 figures, submitted to Phys. Lett.

System size dependence of strange particle yields and spectra at sqrt(s)=17.3 GeV

Yields and spectra of strange hadrons (K+, K-, phi, Lambda and Antilambda) as well as of charged pions were measured in near central C+C and Si+Si collisions at 158 AGeV beam energy with the NA49 detector. Together with earlier data for p+p, S+S and Pb+Pb reactions the system size dependence can be studied. Relative strangeness production rises fast and saturates at about 60 participating nucleons; the net hyperon spectra show an increasing shift towards midrapidity for larger colliding nuclei. An interpretation based on the formation of coherent systems of increasing volume is proposed. The transverse mass spectra can be described by a blast wave ansatz. Increasing flow velocity is accompanied by decreasing temperatures for both kinetic and chemical freeze out. The increasing gap between inelastic and elastic decoupling leaves space for rescattering.Comment: 8 pages, 6 figures, Proceedings of the Hot Quarks 2004 worksho

Two-proton correlations from 158 AGeV Pb+Pb central collisions

The two-proton correlation function at midrapidity from Pb+Pb central collisions at 158 AGeV has been measured by the NA49 experiment. The results are compared to model predictions from static thermal Gaussian proton source distributions and transport models RQMD and VENUS. An effective proton source size is determined by minimizing CHI-square/ndf between the correlation functions of the data and those calculated for the Gaussian sources, yielding 3.85 +-0.15(stat.) +0.60-0.25(syst.) fm. Both the RQMD and the VENUS model are consistent with the data within the error in the correlation peak region.Comment: RevTeX style, 6 pages, 4 figures, 1 table. More discussion are added about the structure on the tail of the correlation function. The systematic error is revised. To appear in Phys. Lett.

Event-by-Event Fluctuations of Particle Ratios in Central Pb+Pb Collisions at 20 to 158 AGeV

In the vicinity of the QCD phase transition, critical fluctuations have been predicted to lead to non-statistical fluctuations of particle ratios, depending on the nature of the phase transition. Recent results of the NA49 energy scan program show a sharp maximum of the ratio of K+ to Pi+ yields in central Pb+Pb collisions at beam energies of 20-30 AGeV. This observation has been interpreted as an indication of a phase transition at low SPS energies. We present first results on event-by-event fluctuations of the kaon to pion and proton to pion ratios at beam energies close to this maximum.Comment: 4 pages, 4 figures, Quark Matter 2004 proceeding