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

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

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

Cross-validation and Peeling Strategies for Survival Bump Hunting using Recursive Peeling Methods

We introduce a framework to build a survival/risk bump hunting model with a censored time-to-event response. Our Survival Bump Hunting (SBH) method is based on a recursive peeling procedure that uses a specific survival peeling criterion derived from non/semi-parametric statistics such as the hazards-ratio, the log-rank test or the Nelson-Aalen estimator. To optimize the tuning parameter of the model and validate it, we introduce an objective function based on survival or prediction-error statistics, such as the log-rank test and the concordance error rate. We also describe two alternative cross-validation techniques adapted to the joint task of decision-rule making by recursive peeling and survival estimation. Numerical analyses show the importance of replicated cross-validation and the differences between criteria and techniques in both low and high-dimensional settings. Although several non-parametric survival models exist, none addresses the problem of directly identifying local extrema. We show how SBH efficiently estimates extreme survival/risk subgroups unlike other models. This provides an insight into the behavior of commonly used models and suggests alternatives to be adopted in practice. Finally, our SBH framework was applied to a clinical dataset. In it, we identified subsets of patients characterized by clinical and demographic covariates with a distinct extreme survival outcome, for which tailored medical interventions could be made. An R package `PRIMsrc` is available on CRAN and GitHub.Comment: Keywords: Exploratory Survival/Risk Analysis, Survival/Risk Estimation & Prediction, Non-Parametric Method, Cross-Validation, Bump Hunting, Rule-Induction Metho