Adaptive Bayesian estimation in indirect Gaussian sequence space models

In an indirect Gaussian sequence space model lower and upper bounds are derived for the concentration rate of the posterior distribution of the parameter of interest shrinking to the parameter value $\theta^\circ$ that generates the data. While this establishes posterior consistency, however, the concentration rate depends on both $\theta^\circ$ and a tuning parameter which enters the prior distribution. We first provide an oracle optimal choice of the tuning parameter, i.e., optimized for each $\theta^\circ$ separately. The optimal choice of the prior distribution allows us to derive an oracle optimal concentration rate of the associated posterior distribution. Moreover, for a given class of parameters and a suitable choice of the tuning parameter, we show that the resulting uniform concentration rate over the given class is optimal in a minimax sense. Finally, we construct a hierarchical prior that is adaptive. This means that, given a parameter $\theta^\circ$ or a class of parameters, respectively, the posterior distribution contracts at the oracle rate or at the minimax rate over the class. Notably, the hierarchical prior does not depend neither on $\theta^\circ$ nor on the given class. Moreover, convergence of the fully data-driven Bayes estimator at the oracle or at the minimax rate is established

Adaptive estimation of linear functionals in functional linear models

We consider the estimation of the value of a linear functional of the slope parameter in functional linear regression, where scalar responses are modeled in dependence of random functions. In Johannes and Schenk [2010] it has been shown that a plug-in estimator based on dimension reduction and additional thresholding can attain minimax optimal rates of convergence up to a constant. However, this estimation procedure requires an optimal choice of a tuning parameter with regard to certain characteristics of the slope function and the covariance operator associated with the functional regressor. As these are unknown in practice, we investigate a fully data-driven choice of the tuning parameter based on a combination of model selection and Lepski's method, which is inspired by the recent work of Goldenshluger and Lepski [2011]. The tuning parameter is selected as the minimizer of a stochastic penalized contrast function imitating Lepski's method among a random collection of admissible values. We show that this adaptive procedure attains the lower bound for the minimax risk up to a logarithmic factor over a wide range of classes of slope functions and covariance operators. In particular, our theory covers point-wise estimation as well as the estimation of local averages of the slope parameter

On large-scale diagonalization techniques for the Anderson model of localization

We propose efficient preconditioning algorithms for an eigenvalue problem arising in quantum physics, namely the computation of a few interior eigenvalues and their associated eigenvectors for large-scale sparse real and symmetric indefinite matrices of the Anderson model of localization. We compare the Lanczos algorithm in the 1987 implementation by Cullum and Willoughby with the shift-and-invert techniques in the implicitly restarted Lanczos method and in the Jacobi–Davidson method. Our preconditioning approaches for the shift-and-invert symmetric indefinite linear system are based on maximum weighted matchings and algebraic multilevel incomplete LDLT factorizations. These techniques can be seen as a complement to the alternative idea of using more complete pivoting techniques for the highly ill-conditioned symmetric indefinite Anderson matrices. We demonstrate the effectiveness and the numerical accuracy of these algorithms. Our numerical examples reveal that recent algebraic multilevel preconditioning solvers can accelerate the computation of a large-scale eigenvalue problem corresponding to the Anderson model of localization by several orders of magnitude

A steerable UV laser system for the calibration of liquid argon time projection chambers

A number of liquid argon time projection chambers (LAr TPC's) are being build or are proposed for neutrino experiments on long- and short baseline beams. For these detectors a distortion in the drift field due to geometrical or physics reasons can affect the reconstruction of the events. Depending on the TPC geometry and electric drift field intensity this distortion could be of the same magnitude as the drift field itself. Recently, we presented a method to calibrate the drift field and correct for these possible distortions. While straight cosmic ray muon tracks could be used for calibration, multiple coulomb scattering and momentum uncertainties allow only a limited resolution. A UV laser instead can create straight ionization tracks in liquid argon, and allows one to map the drift field along different paths in the TPC inner volume. Here we present a UV laser feed-through design with a steerable UV mirror immersed in liquid argon that can point the laser beam at many locations through the TPC. The straight ionization paths are sensitive to drift field distortions, a fit of these distortion to the linear optical path allows to extract the drift field, by using these laser tracks along the whole TPC volume one can obtain a 3D drift field map. The UV laser feed-through assembly is a prototype of the system that will be used for the MicroBooNE experiment at the Fermi National Accelerator Laboratory (FNAL)

Measurement of the drift field in the ARGONTUBE LAr TPC with 266~nm pulsed laser beams

ARGONTUBE is a liquid argon time projection chamber (LAr TPC) with a drift field generated in-situ by a Greinacher voltage multiplier circuit. We present results on the measurement of the drift-field distribution inside ARGONTUBE using straight ionization tracks generated by an intense UV laser beam. Our analysis is based on a simplified model of the charging of a multi-stage Greinacher circuit to describe the voltages on the field cage rings

Experimental study of electric breakdowns in liquid argon at centimeter scale

In this paper we present results on measurements of the dielectric strength of liquid argon near its boiling point and cathode-anode distances in the range of 0.1 mm to 40 mm with spherical cathode and plane anode. We show that at such distances the applied electric field at which breakdowns occur is as low as 40 kV/cm. Flash-overs across the ribbed dielectric of the high voltage feed-through are observed for a length of 300 mm starting from a voltage of 55 kV. These results contribute to set reference for the breakdown-free design of ionization detectors, such as Liquid Argon Time Projection Chambers (LAr TPC)

Performance of cryogenic charge readout electronics with the ARGONTUBE LAr TPC

ARGONTUBE is a liquid argon time projection chamber (TPC) with an electron drift length of up to 5 m equipped with cryogenic charge-sensitive preamplifiers. In this work, we present results on its performance, including a comparison of the new cryogenic charge-sensitive preamplifiers with the previously used room-temperature-operated charge preamplifiers

A meta-analysis of individual participant data reveals an association between circulating levels of IGF-I and prostate cancer risk

The role of insulin-like growth factors (IGF) in prostate cancer development is not fully understood. To investigate the association between circulating concentrations of IGFs (IGF-I, IGF-II, IGFBP-1, IGFBP-2, and IGFBP-3) and prostate cancer risk, we pooled individual participant data from 17 prospective and two cross-sectional studies, including up to 10,554 prostate cancer cases and 13,618 control participants. Conditional logistic regression was used to estimate the ORs for prostate cancer based on the study-specific fifth of each analyte. Overall, IGF-I, IGF-II, IGFBP-2, and IGFBP-3 concentrations were positively associated with prostate cancer risk (Ptrend all ≤ 0.005), and IGFBP-1 was inversely associated weakly with risk (Ptrend = 0.05). However, heterogeneity between the prospective and cross-sectional studies was evident (Pheterogeneity = 0.03), unless the analyses were restricted to prospective studies (with the exception of IGF-II, Pheterogeneity = 0.02). For prospective studies, the OR for men in the highest versus the lowest fifth of each analyte was 1.29 (95% confidence interval, 1.16-1.43) for IGF-I, 0.81 (0.68-0.96) for IGFBP-1, and 1.25 (1.12-1.40) for IGFBP-3. These associations did not differ significantly by time-to-diagnosis or tumor stage or grade. After mutual adjustment for each of the other analytes, only IGF-I remained associated with risk. Our collaborative study represents the largest pooled analysis of the relationship between prostate cancer risk and circulating concentrations of IGF-I, providing strong evidence that IGF-I is highly likely to be involved in prostate cancer development