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ALICE (A Large Ion Collider Experiment), is the dedicated heavy-ion experiment at the Large Hadron Collider (LHC) at CERN. It is optimised to reconstruct and identify the particles created in a lead-lead collision with a centre of mass energy of 5.5TeV. The main tracking detector is a large-volume time-projection chamber (TPC). With an active volume of about 88m^3 and a total readout area of 32.5m^2 it is the most challenging TPC ever build. A central electrode divides the 5m long detector into two drift regions. Each readout side is subdivided into 18 inner and 18 outer multi-wire proportional read-out chambers. The readout area is subdivide into 557568 pads, where each pad is read out by and electronics chanin. A complex calibration is needed in order to reach the design position-resolution of the reconstructed particle tracks of about 200um. One part of the calibration lies in understanding the electronic-response. The work at hand presents results of the pedestal and noise behaviour of the front-end electronics (FEE), measurements of the pulse-shaping properties of the FEE using results obtained with a calibration pulser and measurements performed with the laser-calibration system. The data concerned were taken during two phases of the TPC commissioning. First measurements were performed in the clean room where the TPC was built. After the TPC was moved underground and built into the experiment, a second round of commissioning took place. Noise measurements in the clean room revealed a very large fraction of pads with noise values larger than the design specifications. The unexpected high noise values could be explained by the 'ground bounce' effect. Two modifications helped to reduce this effect: A desynchronisation in the the start of the readout of groups of channels and a modification in the grounding scheme of the FEE. Further noise measurements were carried out after the TPC has been moved to the experimental area underground. Here even a larger fraction of channels showed too large noise values. This could be traced back to a common mode current injected by the electronics power supplies. To study the shaping properties of the FEE a calibration pulser was used. To generate signals in the FEE a pulse is injected to the cathode wires of the read-out chambers. Due to manufacturing tolerances slight channel-by-channel variations of the shaping properties are expected. This effects the determination of the arrival time as well as the measured integral signal of the induced charge and has to be corrected. The measured arrival time variations follow a Gaussian distribution with a width (sigma) of 6.2ns. This corresponds to an error of the cluster position of about 170um. The charge variations are on the level of 2.8%. In order to reach the intrinsic resolution on the measurement of the specific energy loss of the particles (6%) those variations have to be taken into account. The photons of the laser-calibration system are energetic enough to emit photo electrons off metallic surfaces. Most interesting for the detector calibration are photo electrons from the central electrode. The laser light is intense enough to get a signal in all readout channels of the TPC. Since the central electrode is a smooth surface, differences in the arrival time between sectors reveal mechanical displacements of the readout sectors and can be used to correct for this effect. In addition the measurements can be used to determine the electron drift velocity in the TPC gas. The drift velocity measurements have shown a vertical as well as a radial gradient. The first can be explained by the temperature gradient, which naturally builds up in the 5m high detector. The second gradient is most probably caused by a relative conical deformation of the readout plane and the central electrode.
An optimized Bayesian hierarchical two-parameter logistic model for small-sample item calibration
(2019)
Accurate item calibration in models of item response theory (IRT) requires rather large samples. For instance, N > 500 respondents are typically recommended for the two-parameter logistic (2PL) model. Hence, this model is considered a large-scale application, and its use in small-sample contexts is limited. Hierarchical Bayesian approaches are frequently proposed to reduce the sample size requirements of the 2PL. This study compared the small-sample performance of an optimized Bayesian hierarchical 2PL (H2PL) model to its standard inverse Wishart specification, its nonhierarchical counterpart, and both unweighted and weighted least squares estimators (ULSMV and WLSMV) in terms of sampling efficiency and accuracy of estimation of the item parameters and their variance components. To alleviate shortcomings of hierarchical models, the optimized H2PL (a) was reparametrized to simplify the sampling process, (b) a strategy was used to separate item parameter covariances and their variance components, and (c) the variance components were given Cauchy and exponential hyperprior distributions. Results show that when combining these elements in the optimized H2PL, accurate item parameter estimates and trait scores are obtained even in sample sizes as small as N = 100. This indicates that the 2PL can also be applied to smaller sample sizes encountered in practice. The results of this study are discussed in the context of a recently proposed multiple imputation method to account for item calibration error in trait estimation.