Brownian Confidence Bands on Monte Carlo Output

International audienceWhen considering a Monte Carlo estimation procedure, the path produced by successive partial estimates is often used as a guide for informal convergence diagnostics. However the confidence region associated with that path cannot be derived simplistically from the confidence interval for the estimate itself. An asymptotically correct approach can be based on the Brownian motion approximation of the path, but no exact formula for the corresponding area-minimizing confidence region is yet known. We construct proxy regions based on local time arguments and consider numerical approximations. These are then available for a more incisive assessment of the Monte Carlo procedure and thence of the estimate itself

Minimum variance importance sampling via Population Monte Carlo

International audienceVariance reduction has always been a central issue in Monte Carlo experiments. Population Monte Carlo can be used to this effect, in that a mixture of importance functions, called a D-kernel, can be iteratively optimised to achieve the minimum asymptotic variance for a function of interest among all possible mixtures. The implementation of this iterative scheme is illustrated for the computation of the price of a European option in the Cox-Ingersoll-Ross model

Convergence of adaptive sampling schemes

International audienceIn the design of efficient simulation algorithms, one is often beset with a poor choice of proposal distributions. Although the performances of a given kernel can clarify how adequate it is for the problem at hand, a permanent on-line modification of kernels causes concerns about the validity of the resulting algorithm. While the issue is quite complex and most often intractable for MCMC algorithms, the equivalent version for importance sampling algorithms can be validated quite precisely. We derive sufficient convergence conditions for a wide class of population Monte Carlo algorithms and show that Rao-Blackwellized versions asymptotically achieve an optimum in terms of a Kullback divergence criterion, while more rudimentary versions simply do not benefit from repeated updating

Somatotypes trajectories during adulthood and their association with COPD phenotypes

Rationale: Chronic obstructive pulmonary disease (COPD) comprises distinct phenotypes, all characterised by airflow limitation. Objectives: We hypothesised that somatotype changes - as a surrogate of adiposity - from early adulthood follow different trajectories to reach distinct phenotypes. Methods: Using the validated Stunkard''s Pictogram, 356 COPD patients chose the somatotype that best reflects their current body build and those at ages 18, 30, 40 and 50 years. An unbiased group-based trajectory modelling was used to determine somatotype trajectories. We then compared the current COPD-related clinical and phenotypic characteristics of subjects belonging to each trajectory. Measurements and main results: At 18 years of age, 88% of the participants described having a lean or medium somatotype (estimated body mass index (BMI) between 19 and 23 kg.m(-2)) while the other 12% a heavier somatotype (estimated BMI between 25 and 27 kg.m(-2)). From age 18 onwards, five distinct trajectories were observed. Four of them demonstrating a continuous increase in adiposity throughout adulthood with the exception of one, where the initial increase was followed by loss of adiposity after age 40. Patients with this trajectory were primarily females with low BMI and D-LCO (diffusing capacity of the lung for carbon monoxide). A persistently lean trajectory was seen in 14% of the cohort. This group had significantly lower forced expiratory volume in 1 s (FEV1), D-LCO, more emphysema and a worse BODE (BMI, airflow obstruction, dyspnoea and exercise capacity) score thus resembling the multiple organ loss of tissue (MOLT) phenotype. Conclusions: COPD patients have distinct somatotype trajectories throughout adulthood. Those with the MOLT phenotype maintain a lean trajectory throughout life. Smoking subjects with this lean phenotype in early adulthood deserve particular attention as they seem to develop more severe COPD

MCMC implementation for Bayesian hidden semi-Markov models with illustrative applications

Copyright © Springer 2013. The final publication is available at Springer via http://dx.doi.org/10.1007/s11222-013-9399-zHidden Markov models (HMMs) are flexible, well established models useful in a diverse range of applications. However, one potential limitation of such models lies in their inability to explicitly structure the holding times of each hidden state. Hidden semi-Markov models (HSMMs) are more useful in the latter respect as they incorporate additional temporal structure by explicit modelling of the holding times. However, HSMMs have generally received less attention in the literature, mainly due to their intensive computational requirements. Here a Bayesian implementation of HSMMs is presented. Recursive algorithms are proposed in conjunction with Metropolis-Hastings in such a way as to avoid sampling from the distribution of the hidden state sequence in the MCMC sampler. This provides a computationally tractable estimation framework for HSMMs avoiding the limitations associated with the conventional EM algorithm regarding model flexibility. Performance of the proposed implementation is demonstrated through simulation experiments as well as an illustrative application relating to recurrent failures in a network of underground water pipes where random effects are also included into the HSMM to allow for pipe heterogeneity

Somatotypes trajectories during adulthood and their association with COPD phenotypes

Rationale: Chronic obstructive pulmonary disease (COPD) comprises distinct phenotypes, all characterised by airflow limitation. Objectives: We hypothesised that somatotype changes – as a surrogate of adiposity – from early adulthood follow different trajectories to reach distinct phenotypes. Methods: Using the validated Stunkard’s Pictogram, 356 COPD patients chose the somatotype that best reflects their current body build and those at ages 18, 30, 40 and 50 years. An unbiased group-based trajectory modelling was used to determine somatotype trajectories. We then compared the current COPD-related clinical and phenotypic characteristics of subjects belonging to each trajectory. Measurements and main results: At 18 years of age, 88% of the participants described having a lean or medium somatotype (estimated body mass index (BMI) between 19 and 23 kg·m−2 ) while the other 12% a heavier somatotype (estimated BMI between 25 and 27 kg·m−2 ). From age 18 onwards, five distinct trajectories were observed. Four of them demonstrating a continuous increase in adiposity throughout adulthood with the exception of one, where the initial increase was followed by loss of adiposity after age 40. Patients with this trajectory were primarily females with low BMI and DLCO (diffusing capacity of the lung for carbon monoxide). A persistently lean trajectory was seen in 14% of the cohort. This group had significantly lower forced expiratory volume in 1 s (FEV1), DLCO, more emphysema and a worse BODE (BMI, airflow obstruction, dyspnoea and exercise capacity) score thus resembling the multiple organ loss of tissue (MOLT) phenotype. Conclusions: COPD patients have distinct somatotype trajectories throughout adulthood. Those with the MOLT phenotype maintain a lean trajectory throughout life. Smoking subjects with this lean phenotype in early adulthood deserve particular attention as they seem to develop more severe COPD

Hadron Energy Reconstruction for the ATLAS Calorimetry in the Framework of the Non-parametrical Method

This paper discusses hadron energy reconstruction for the ATLAS barrel prototype combined calorimeter (consisting of a lead-liquid argon electromagnetic part and an iron-scintillator hadronic part) in the framework of the non-parametrical method. The non-parametrical method utilizes only the known $e/h$ ratios and the electron calibration constants and does not require the determination of any parameters by a minimization technique. Thus, this technique lends itself to an easy use in a first level trigger. The reconstructed mean values of the hadron energies are within $\pm 1$ of the true values and the fractional energy resolution is $[(58\pm3)/\sqrt{E}+(2.5\pm0.3)$. The value of the $e/h$ ratio obtained for the electromagnetic compartment of the combined calorimeter is $1.74\pm0.04$ and agrees with the prediction that $e/h > 1.7$ for this electromagnetic calorimeter. Results of a study of the longitudinal hadronic shower development are also presented. The data have been taken in the H8 beam line of the CERN SPS using pions of energies from 10 to 300 GeV.Comment: 33 pages, 13 figures, Will be published in NIM

Measurement of the polarisation of W bosons produced with large transverse momentum in pp collisions at sqrt(s) = 7 TeV with the ATLAS experiment

This paper describes an analysis of the angular distribution of W->enu and W->munu decays, using data from pp collisions at sqrt(s) = 7 TeV recorded with the ATLAS detector at the LHC in 2010, corresponding to an integrated luminosity of about 35 pb^-1. Using the decay lepton transverse momentum and the missing transverse energy, the W decay angular distribution projected onto the transverse plane is obtained and analysed in terms of helicity fractions f0, fL and fR over two ranges of W transverse momentum (ptw): 35 < ptw < 50 GeV and ptw > 50 GeV. Good agreement is found with theoretical predictions. For ptw > 50 GeV, the values of f0 and fL-fR, averaged over charge and lepton flavour, are measured to be : f0 = 0.127 +/- 0.030 +/- 0.108 and fL-fR = 0.252 +/- 0.017 +/- 0.030, where the first uncertainties are statistical, and the second include all systematic effects.Comment: 19 pages plus author list (34 pages total), 9 figures, 11 tables, revised author list, matches European Journal of Physics C versio

Observation of a new chi_b state in radiative transitions to Upsilon(1S) and Upsilon(2S) at ATLAS

The chi_b(nP) quarkonium states are produced in proton-proton collisions at the Large Hadron Collider (LHC) at sqrt(s) = 7 TeV and recorded by the ATLAS detector. Using a data sample corresponding to an integrated luminosity of 4.4 fb^-1, these states are reconstructed through their radiative decays to Upsilon(1S,2S) with Upsilon->mu+mu-. In addition to the mass peaks corresponding to the decay modes chi_b(1P,2P)->Upsilon(1S)gamma, a new structure centered at a mass of 10.530+/-0.005 (stat.)+/-0.009 (syst.) GeV is also observed, in both the Upsilon(1S)gamma and Upsilon(2S)gamma decay modes. This is interpreted as the chi_b(3P) system.Comment: 5 pages plus author list (18 pages total), 2 figures, 1 table, corrected author list, matches final version in Physical Review Letter

Search for displaced vertices arising from decays of new heavy particles in 7 TeV pp collisions at ATLAS

We present the results of a search for new, heavy particles that decay at a significant distance from their production point into a final state containing charged hadrons in association with a high-momentum muon. The search is conducted in a pp-collision data sample with a center-of-mass energy of 7 TeV and an integrated luminosity of 33 pb^-1 collected in 2010 by the ATLAS detector operating at the Large Hadron Collider. Production of such particles is expected in various scenarios of physics beyond the standard model. We observe no signal and place limits on the production cross-section of supersymmetric particles in an R-parity-violating scenario as a function of the neutralino lifetime. Limits are presented for different squark and neutralino masses, enabling extension of the limits to a variety of other models.Comment: 8 pages plus author list (20 pages total), 8 figures, 1 table, final version to appear in Physics Letters