Inference on Treatment Effects After Selection Amongst High-Dimensional Controls

We propose robust methods for inference on the effect of a treatment variable on a scalar outcome in the presence of very many controls. Our setting is a partially linear model with possibly non-Gaussian and heteroscedastic disturbances. Our analysis allows the number of controls to be much larger than the sample size. To make informative inference feasible, we require the model to be approximately sparse; that is, we require that the effect of confounding factors can be controlled for up to a small approximation error by conditioning on a relatively small number of controls whose identities are unknown. The latter condition makes it possible to estimate the treatment effect by selecting approximately the right set of controls. We develop a novel estimation and uniformly valid inference method for the treatment effect in this setting, called the "post-double-selection" method. Our results apply to Lasso-type methods used for covariate selection as well as to any other model selection method that is able to find a sparse model with good approximation properties. The main attractive feature of our method is that it allows for imperfect selection of the controls and provides confidence intervals that are valid uniformly across a large class of models. In contrast, standard post-model selection estimators fail to provide uniform inference even in simple cases with a small, fixed number of controls. Thus our method resolves the problem of uniform inference after model selection for a large, interesting class of models. We illustrate the use of the developed methods with numerical simulations and an application to the effect of abortion on crime rates

Influence of solvent quality on effective pair potentials between polymers in solution

Solutions of interacting linear polymers are mapped onto a system of ``soft'' spherical particles interacting via an effective pair potential. This coarse-graining reduces the individual monomer-level description to a problem involving only the centers of mass (CM) of the polymer coils. The effective pair potentials are derived by inverting the CM pair distribution function, generated in Monte Carlo simulations, using the hypernetted chain (HNC) closure. The method, previously devised for the self-avoiding walk model of polymers in good solvent, is extended to the case of polymers in solvents of variable quality by adding a finite nearest-neighbor monomer-monomer attraction to the previous model and varying the temperature. The resulting effective pair potential is found to depend strongly on temperature and polymer concentration. At low concentration the effective interaction becomes increasingly attractive as the temperature decreases, eventually violating thermodynamic stability criteria. However, as polymer concentration is increased at fixed temperature, the effective interaction reverts to mostly repulsive behavior. These issues help illustrate some fundamental difficulties encountered when coarse-graining complex systems via effective pair potentials.Comment: 15 pages, 12 figures (one added in revised version), revTeX

Relating monomer to centre-of-mass distribution functions in polymer solutions

A relationship between the measurable monomer-monomer structure factor, and the centre-of-mass (CM) structure factor of dilute or semi-dilute polymer solutions is derived from Ornstein-Zernike relations within the ``polymer reference interaction site model'' (PRISM) formalism, by considering the CM of each polymer as an auxiliary site and neglecting direct correlations between the latter and the CM and monomers of neighbouring polymers. The predictions agree well with Monte Carlo data for self-avoiding walk polymers, and are considerably more accurate than the predictions of simple factorization approximations.Comment: uses eps.cls, v2 is close to final published versio

The Impact of Simulation Sequencing on Perceived Clinical Decision Making

An emerging nursing education trend is to utilize simulated learning experiences as a means to optimize competency and decision making skills. The purpose of this study was to examine differences in students\u27 perception of clinical decision making and clinical decision making-related self-confidence and anxiety based on the sequence (order) in which they participated in a block of simulated versus hospital-based learning experiences. A quasi-experimental crossover design was used. Between and within group differences were found relative to self-confidence with the decision making process. When comparing groups, at baseline the simulation followed by hospital group had significantly higher self-confidence scores, however, at 14-weeks both groups were not significantly different. Significant within group differences were found in the simulation followed by hospital group only, demonstrating a significant decrease in clinical decision making related anxiety across the semester. Finally, there were no significant difference in; perceived clinical decision making within or between the groups at the two measurement points. Preliminary findings suggest that simulated learning experiences can be offered with alternating sequences without impacting the process, anxiety or confidence with clinical decision making. This study provides beginning evidence to guide curriculum development and allow flexibility based on student needs and available resources

First measurement of cluster temperature using the thermal Sunyaev-Zeldovich effect

We discuss a new method of finding the cluster temperatures which is independent of distance and therefore very useful for distant clusters. The hot gas of electrons in clusters of galaxies scatters and distorts the cosmic microwave background radiation in a well determined way. This Sunyaev-Zel'dovich (SZ) effect is a useful tool for extracting information about clusters such as their peculiar radial velocity and optical depth. Here we show how the temperature of the cluster can be inferred from the SZ effect, in principle without use of X-ray data. We use recent millimetre observation of Abell 2163 to determine for the first time a cluster temperature using SZ observations only. The result T_e = 26^+34_-19 keV at 68% confidence level (at 95% c.l. we find T>1.5 keV) is in reasonable agreement with the X-ray results, T_e =12.4^+2.8_-1.9 keV.Comment: 7 pages, 2 figure

Spectral distortion of cosmic background radiation by scattering on hot electrons. Exact calculations

The spectral distortion of the cosmic background radiation produced by the inverse Compton scattering on hot electrons in clusters of galaxies (thermal Sunyaev-Zeldovich effect) is calculated for arbitrary optical depth and electron temperature. The distortion is found by a numerical solution of the exact Boltzmann equation for the photon distribution function. In the limit of small optical depth and low electron temperature our results confirm the previous analyses. In the opposite limits, our method is the only one that permits to make accurate calculations.Comment: 18 pages, 7 figures, to be published in Ap

Osmotic properties of polyethyleneglycols: quantitative features of brush and bulk scaling laws

From glycosylated cell surfaces to sterically stabilized liposomes, polymers attached to membranes attract biological and therapeutic interest. Can the scaling laws of polymer "brushes" describe the physical properties of these coats? We delineate conditions where the Alexander - de Gennes theory of polymer brushes successfully describes the intermembrane distance vs. applied osmotic stress data of Kenworthy et al. for PEG-grafted multilamellar liposomes [Biophys. J. (1995) 68:1921]. We establish that the polymer density and size in the brush must be high enough that, in a bulk solution of equivalent density, the polymer osmotic pressure is independent of polymer molecular weight (the des Cloizeaux semi-dilute regime of bulk polymer solutions). The condition that attached polymers behave as semi-dilute bulk solutions offers a rigorous criterion for brush scaling-law behavior. There is a deep connection between the behaviors of polymer solutions in bulk and polymers grafted to a surface at a density such that neighbors pack to form a uniform brush. In this regime, two-parameter unconstrained fits of the Alexander - de Gennes brush scaling laws yield effective monomer lengths of 3.3 to 3.5 AA, which agree with structural predictions. The fitted distances between grafting sites are larger than expected from the nominal content of PEG-lipids; the chains apparently saturate the surface. Osmotic stress measurements can be used to estimate the actual densities of membrane-grafted polymers.Comment: 26 pages with figure