Prediction Weighted Maximum Frequency Selection

Shrinkage estimators that possess the ability to produce sparse solutions have become increasingly important to the analysis of today's complex datasets. Examples include the LASSO, the Elastic-Net and their adaptive counterparts. Estimation of penalty parameters still presents difficulties however. While variable selection consistent procedures have been developed, their finite sample performance can often be less than satisfactory. We develop a new strategy for variable selection using the adaptive LASSO and adaptive Elastic-Net estimators with $p_n$ diverging. The basic idea first involves using the trace paths of their LARS solutions to bootstrap estimates of maximum frequency (MF) models conditioned on dimension. Conditioning on dimension effectively mitigates overfitting, however to deal with underfitting, these MFs are then prediction-weighted, and it is shown that not only can consistent model selection be achieved, but that attractive convergence rates can as well, leading to excellent finite sample performance. Detailed numerical studies are carried out on both simulated and real datasets. Extensions to the class of generalized linear models are also detailed.Comment: This manuscript contains 41 pages and 14 figure

Spike and slab variable selection: Frequentist and Bayesian strategies

Variable selection in the linear regression model takes many apparent faces from both frequentist and Bayesian standpoints. In this paper we introduce a variable selection method referred to as a rescaled spike and slab model. We study the importance of prior hierarchical specifications and draw connections to frequentist generalized ridge regression estimation. Specifically, we study the usefulness of continuous bimodal priors to model hypervariance parameters, and the effect scaling has on the posterior mean through its relationship to penalization. Several model selection strategies, some frequentist and some Bayesian in nature, are developed and studied theoretically. We demonstrate the importance of selective shrinkage for effective variable selection in terms of risk misclassification, and show this is achieved using the posterior from a rescaled spike and slab model. We also show how to verify a procedure's ability to reduce model uncertainty in finite samples using a specialized forward selection strategy. Using this tool, we illustrate the effectiveness of rescaled spike and slab models in reducing model uncertainty.Comment: Published at http://dx.doi.org/10.1214/009053604000001147 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Shape Instabilities in the Dynamics of a Two-component Fluid Membrane

We study the shape dynamics of a two-component fluid membrane, using a dynamical triangulation monte carlo simulation and a Langevin description. Phase separation induces morphology changes depending on the lateral mobility of the lipids. When the mobility is large, the familiar labyrinthine spinodal pattern is linearly unstable to undulation fluctuations and breaks up into buds, which move towards each other and merge. For low mobilities, the membrane responds elastically at short times, preferring to buckle locally, resulting in a crinkled surface.Comment: 4 pages, revtex, 3 eps figure

A Novel Monte Carlo Approach to the Dynamics of Fluids --- Single Particle Diffusion, Correlation Functions and Phase Ordering of Binary Fluids

We propose a new Monte Carlo scheme to study the late-time dynamics of a 2-dim hard sphere fluid, modeled by a tethered network of hard spheres. Fluidity is simulated by breaking and reattaching the flexible tethers. We study the diffusion of a tagged particle, and show that the velocity autocorrelation function has a long-time $t^{-1}$ tail. We investigate the dynamics of phase separation of a binary fluid at late times, and show that the domain size $R(t)$ grows as $t^{1/2}$ for high viscosity fluids with a crossover to $t^{2/3}$ for low viscosity fluids. Our scheme can accomodate particles interacting with a pair potential $V(r)$,and modified to study dynamics of fluids in three dimensions.Comment: Latex, 4 pages, 4 figure

The Challenges of Conducting Clinical Trials for Patients with Cardiogenic Shock

Cardiogenic shock due to ST-segment elevation myocardial infarction is associated with high morbidity and mortality. Patients in shock are acutely ill, and clinicians may lack equipoise, thus presenting a challenge to developing high-quality evidence to guide practice. This review will summarize these challenges and offer possible solutions

Fence methods for mixed model selection

Many model search strategies involve trading off model fit with model complexity in a penalized goodness of fit measure. Asymptotic properties for these types of procedures in settings like linear regression and ARMA time series have been studied, but these do not naturally extend to nonstandard situations such as mixed effects models, where simple definition of the sample size is not meaningful. This paper introduces a new class of strategies, known as fence methods, for mixed model selection, which includes linear and generalized linear mixed models. The idea involves a procedure to isolate a subgroup of what are known as correct models (of which the optimal model is a member). This is accomplished by constructing a statistical fence, or barrier, to carefully eliminate incorrect models. Once the fence is constructed, the optimal model is selected from among those within the fence according to a criterion which can be made flexible. In addition, we propose two variations of the fence. The first is a stepwise procedure to handle situations of many predictors; the second is an adaptive approach for choosing a tuning constant. We give sufficient conditions for consistency of fence and its variations, a desirable property for a good model selection procedure. The methods are illustrated through simulation studies and real data analysis.Comment: Published in at http://dx.doi.org/10.1214/07-AOS517 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Effectiveness of Silane and Siloxane Treatments on the Superhydrophobicity and Icephobicity of Concrete Surfaces

Icy roads lead to treacherous driving conditions in regions of the U.S., leading to over 450 fatalities per year. De-icing chemicals, such as road salt, leave much to be desired. In this report, commercially available silane, siloxane, and related materials were evaluated as solutions, simple emulsions, and complex emulsions with incorporated particulates, for their effectiveness as superhydrophobic treatments. Through the development and use of a basic impact test, the ease of ice removal (icephobicity) was examined as an application of the targeted superhydrophobicity. A general correlation was found between icephobicity and hydrophobicity, with the amount of ice removed on impact increasing with increasing contact angle. However, the correlation was poor in the high performance region (high contact angle and high ice removal.) Polymethylhydrogensiloxane was a top performer and was more effective when used as a shell type emulsion with silica fume particulates. An aqueous sodium methyl siliconate solution showed good performance for ice loss and contact angle, as did a commercial proprietary emulsion using a diethoxyoctylsilyl trimethylsilyl ester of silicic acid. These materials have sterically available functional groups that can react or associate with the concrete surface and are potentially film-forming. Materials with less reactive functional groups and a lower propensity to film-form did not perform as well

Unsupervised Bump Hunting Using Principal Components

Principal Components Analysis is a widely used technique for dimension reduction and characterization of variability in multivariate populations. Our interest lies in studying when and why the rotation to principal components can be used effectively within a response-predictor set relationship in the context of mode hunting. Specifically focusing on the Patient Rule Induction Method (PRIM), we first develop a fast version of this algorithm (fastPRIM) under normality which facilitates the theoretical studies to follow. Using basic geometrical arguments, we then demonstrate how the PC rotation of the predictor space alone can in fact generate improved mode estimators. Simulation results are used to illustrate our findings.Comment: 24 pages, 9 figure