Penalized Functional Regression,
2010
Johns Hopkins Bloomberg School of Public Health, Department of Biostatistics
Penalized Functional Regression, Jeff Goldsmith, Jennifer Feder, Ciprian M. Crainiceanu, Brian Caffo, Daniel Reich
Johns Hopkins University, Dept. of Biostatistics Working Papers
We develop fast fitting methods for generalized functional linear models. An undersmooth of the functional predictor is obtained by projecting on a large number of smooth eigenvectors and the coefficient function is estimated using penalized spline regression. Our method can be applied to many functional data designs including functions measured with and without error, sparsely or densely sampled. The methods also extend to the case of multiple functional predictors or functional predictors with a natural multilevel structure. Our approach can be implemented using standard mixed effects software and is computationally fast. Our methodology is motivated by a diffusion tensor imaging …
Regression Adjustment And Stratification By Propensty Score In Treatment Effect Estimation,
2010
Johns Hopkins Bloomberg School of Public Health, Department of Biostatistics
Regression Adjustment And Stratification By Propensty Score In Treatment Effect Estimation, Jessica A. Myers, Thomas A. Louis
Johns Hopkins University, Dept. of Biostatistics Working Papers
Propensity score adjustment of effect estimates in observational studies of treatment is a common technique used to control for bias in treatment assignment. In situations where matching on propensity score is not possible or desirable, regression adjustment and stratification are two options. Regression adjustment is used most often and can be highly efficient, but it can lead to biased results when model assumptions are violated. Validity of the stratification approach depends on fewer model assumptions, but is less efficient than regression adjustment when the regression assumptions hold. To investigate these issues, by simulation we compare stratification and regression adjustments. We …
Exploring The Benefits Of Adaptive Sequential Designs In Time-To-Event Endpoint Settings,
2010
Harvard University
Exploring The Benefits Of Adaptive Sequential Designs In Time-To-Event Endpoint Settings, Sarah C. Emerson, Kyle Rudser, Scott S. Emerson
UW Biostatistics Working Paper Series
Sequential analysis is frequently employed to address ethical and financial issues in clinical trials. Sequential analysis may be performed using standard group sequential designs, or, more recently, with adaptive designs that use estimates of treatment effect to modify the maximal statistical information to be collected. In the general setting in which statistical information and clinical trial costs are functions of the number of subjects used, it has yet to be established whether there is any major efficiency advantage to adaptive designs over traditional group sequential designs. In survival analysis, however, statistical information (and hence efficiency) is most closely related to …
Wright State University Fact Sheet, 2009-2010,
2010
Wright State University
Wright State University Fact Sheet, 2009-2010, Office Of Institutional Research & Effectiveness, Wright State University
Wright State University Fact Sheets
The Wright State University Fact Sheet showcasing numbers and statistics for Wright State University including demographics, funding, programs, and employment for the 2009-2010 academic year.
Nonlinear Model Reduction Using Group Proper Orthogonal Decomposition,
2010
Missouri University of Science and Technology
Nonlinear Model Reduction Using Group Proper Orthogonal Decomposition, Benjamin T. Dickinson, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
We propose a new method to reduce the cost of computing nonlinear terms in projec- tion based reduced order models with global basis functions. We develop this method by extending ideas from the group nite element (GFE) method to proper orthogonal decomposition (POD) and call it the group POD method. Here, a scalar two-dimensional Burgers' equation is used as a model problem for the group POD method. Numerical results show that group POD models of Burgers' equation are as accurate and are computationally more e cient than standard POD models of Burgers' equation.
Optimality Of Balanced Proper Orthogonal Decomposition For Data Reconstruction,
2010
Missouri University of Science and Technology
Optimality Of Balanced Proper Orthogonal Decomposition For Data Reconstruction, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
Proper orthogonal decomposition (POD) finds an orthonormal basis yielding an optimal reconstruction of a given dataset. We consider an optimal data reconstruction problem for two general datasets related to balanced POD, which is an algorithm for balanced truncation model reduction for linear systems. We consider balanced POD outside of the linear systems framework, and prove that it solves the optimal data reconstruction problem. the theoretical result is illustrated with an example.
Balanced Pod Algorithm For Robust Control Design For Linear Distributed Parameter Systems,
2010
Missouri University of Science and Technology
Balanced Pod Algorithm For Robust Control Design For Linear Distributed Parameter Systems, John R. Singler, Belinda A. Batten
Mathematics and Statistics Faculty Research & Creative Works
A mathematical model of a physical system is never perfect; therefore, robust control laws are necessary for guaranteed stabilization of the nominal model and also "nearby" systems, including hopefully the actual physical system. We consider the computation of a robust control law for large-scale finite dimensional linear systems and a class of linear distributed parameter systems. The controller is robust with respect to left coprime factor perturbations of the nominal system. We present an algorithm based on balanced proper orthogonal decomposition to compute the nonstandard features of this robust control law. Numerical results are presented for a convection diffusion partial …
Computational Issues In Sensitivity Analysis For 1d Interface Problems,
2010
Missouri University of Science and Technology
Computational Issues In Sensitivity Analysis For 1d Interface Problems, L. G. Davis, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
This paper is concerned with the construction of accurate and e cient computational algorithms for the numerical approximation of sensitivities with respect to a parameter dependent interface location. Motivated by sensitivity analysis with respect to piezoelectric actuator placement on an
Boundary Data Maps For Schrödinger Operators On A Compact Interval,
2010
Missouri University of Science and Technology
Boundary Data Maps For Schrödinger Operators On A Compact Interval, Stephen L. Clark, Fritz Gesztesy, M. Mitrea
Mathematics and Statistics Faculty Research & Creative Works
We provide a systematic study of boundary data maps, that is, 2 x 2 matrix-valued Dirichlet-to-Neumann and more generally, Robin-to-Robin maps, associated with one-dimensional Schrödinger operators on a compact interval [0, R] with separated boundary conditions at 0 and R. Most of our results are formulated in the non-self-adjoint context. Our principal results include explicit representations of these boundary data maps in terms of the resolvent of the underlying Schrödinger operator and the associated boundary trace maps, Krein-type resolvent formulas relating Schrödinger operators corresponding to different (separated) boundary conditions, and a derivation of the Herglotz property of boundary data maps …
High Accuracy Combination Method For Solving The Systems Of Nonlinear Volterra Integral And Integro-Differential Equations With Weakly Singular Kernels Of The Second Kind,
2010
Missouri University of Science and Technology
High Accuracy Combination Method For Solving The Systems Of Nonlinear Volterra Integral And Integro-Differential Equations With Weakly Singular Kernels Of The Second Kind, Xiaoming He, Lu Pan, Tao Lü
Mathematics and Statistics Faculty Research & Creative Works
This paper presents a high accuracy combination algorithm for solving the systems of nonlinear Volterra integral and integro-differential equations with weakly singular kernels of the second kind. Two quadrature algorithms for solving the systems are discussed, which possess high accuracy order and the asymptotic expansion of the errors. By means of combination algorithm, we may obtain a numerical solution with higher accuracy order than the original two quadrature algorithms. Moreover an a posteriori error estimation for the algorithm is derived. Both of the theory and the numerical examples show that the algorithm is effective and saves storage capacity and computational …
The Hodrick-Prescott Filter: A Special Case Of Penalized Spline Smoothing,
2010
Missouri University of Science and Technology
The Hodrick-Prescott Filter: A Special Case Of Penalized Spline Smoothing, Robert Paige L., A. A. Trindade
Mathematics and Statistics Faculty Research & Creative Works
We prove that the Hodrick-Prescott Filter (HPF), a commonly used method for smoothing econometric time series, is a special case of a linear penalized spline model with knots placed at all observed time points (except the first and last) and uncorrelated residuals. This equivalence then furnishes a rich variety of existing data-driven parameter estimation methods, particularly restricted maximum likelihood (REML) and generalized cross-validation (GCV). This has profound implications for users of HPF who have hitherto typically relied on subjective choice, rather than estimation, for the smoothing parameter. By viewing estimates as roots of an appropriate quadratic estimating equation, we also …
Incorporating Genome Annotation In The Statistical Analysis Of Genomic And Epigenomic Tiling Array Data,
2010
Missouri University of Science and Technology
Incorporating Genome Annotation In The Statistical Analysis Of Genomic And Epigenomic Tiling Array Data, Gayla R. Olbricht
Mathematics and Statistics Faculty Research & Creative Works
"A wealth of information and technologies are currently available for the genomewide investigation of many types of biological phenomena. Genomic annotation databases provide information about the DNA sequence of a particular organism and give locations of different types of genomic elements, such as the exons and introns of genes. Microarrays are a powerful type of technology that make use of DNA sequence information to investigate different types of biological phenomena on a genome-wide level. Tiling arrays are a unique type of microarray that provide unbiased, highdensity coverage of a genomic region, making them well suited for many applications, such as …
The Beta Maxwell Distribution,
2010
Marshall University
The Beta Maxwell Distribution, Grace Ebunoluwa Amusan
Theses, Dissertations and Capstones
In this work we considered a general class of distributions gener- ated from the logit of the beta random variable. We looked at various works that have been done and discussed some of the results that were obtained. Special cases of this class include the beta-normal distribution, the beta-exponential distribution, the beta-Gumbell distribution, the beta-Weibull distribution, the beta-Pareto distribution and the beta-Rayleigh distribution. We looked at the probability distribution functions of each of these distributions and also look at some of their properties. Another special case of this family, a three-parameter beta-Maxwell distribution was dened and studied. Various properties of …
Periodic Solutions Of Neutral Delay Integral Equations Of Advanced Type,
2010
University of Dayton
Periodic Solutions Of Neutral Delay Integral Equations Of Advanced Type, Muhammad Islam, Nasrin Sultana, James Booth
Mathematics Faculty Publications
We study the existence of continuous periodic solutions of a neutral delay integral equation of advanced type. In the analysis we employ three fixed point theorems: Banach, Krasnosel'skii, and Krasnosel'skii-Schaefer. Krasnosel'skii-Schaefer fixed point theorem requires an a priori bound on all solutions. We employ a Liapunov type method to obtain such bound.
Principal Component Analysis And Biochemical Characterization Of Protein And
Starch Reveal Primary Targets For Improving Sorghum Grain,
2010
University of California - Berkeley
Principal Component Analysis And Biochemical Characterization Of Protein And Starch Reveal Primary Targets For Improving Sorghum Grain, Joshua H. Wong, D. B. Marx, Jeff D. Wilson, Bob B. Buchanan, Peggy G. Lemaux, Jeffrey F. Pedersen
Department of Statistics: Faculty Publications
Limited progress has been made on genetic improvement of the digestibility of sorghum grain because of variability among different varieties. In this study, we applied multiple techniques to assess digestibility of grain from 18 sorghum lines to identify major components responsible for variability. We also identified storage proteins and enzymes as potential targets for genetic modification to improve digestibility. Results from principal component analysis revealed that content of amylose and total starch, together with protein digestibility (PD), accounted for 94% of variation in digestibility. Control of amylose content is understood and manageable. Up-regulation of genes associated with starch accumulation is …
Reference Priors For Exponential Families
With Increasing Dimension,
2010
University of Nebraska-Lincoln
Reference Priors For Exponential Families With Increasing Dimension, Bertrand S. Clarke, Subhashis Ghosal
Department of Statistics: Faculty Publications
In this article, we establish the asymptotic normality of the posterior distribution for the natural parameter in an exponential family based on independent and identically distributed data. The mode of convergence is expected Kullback-Leibler distance and the number of parameters p is increasing with the sample size n. Using this, we give an asymptotic expansion of the Shannon mutual information valid when p = pn increases at a sufficiently slow rate. The second term in the asymptotic expansion is the largest term that depends on the prior and can be optimized to give Jeffreys’ prior as the reference prior in …
Desiderata For A Predictive Theory Of Statistics,
2010
University of Miami
Desiderata For A Predictive Theory Of Statistics, Bertrand Clarke
Department of Statistics: Faculty Publications
In many contexts the predictive validation of models or their associated prediction strategies is of greater importance than model identification which may be practically impossible. This is particularly so in fields involving complex or high dimensional data where model selection, or more generally predictor selection is the main focus of effort. This paper suggests a unified treatment for predictive analyses based on six 'desiderata'. These desiderata are an effort to clarify what criteria a good predictive theory of statistics should satisfy.
Mathematical Themes In Economics, Machine Learning, And Bioinformatics,
2010
Western Kentucky University
Mathematical Themes In Economics, Machine Learning, And Bioinformatics, Matt Bogard
Economics Faculty Publications
Graduate students in economics are often introduced to some very useful mathematical tools that many outside the discipline may not associate with training in economics. This essay looks at some of these tools and concepts, including constrained optimization, separating hyperplanes, supporting hyperplanes, and ‘duality.’ Applications of these tools are explored including topics from machine learning and bioinformatics.
Sustainable Agriculture Bibliography,
2010
Western Kentucky University
Sustainable Agriculture Bibliography, Matt Bogard
Agriculture Department Seminar Series
An annotated bibliography related to the sustainability of biotechnology and pharmaceutical technologies used in modern agriculture.
Item Order Effects On Attitude Measures,
2010
University of Denver
Item Order Effects On Attitude Measures, Pei-Hua Chen
Electronic Theses and Dissertations
The purpose of this dissertation was to examine the effects of altered item order on attitude measures for both computerized adaptive and conventional survey formats. Based on items modified from a dissertation/thesis completion survey (Green & Kluever, 1997) with three scales, three survey versions were generated with items ordered by difficulty as hard-to-easy (H-E), easy-to-hard (E-H), and five medium trait level items presented first followed by randomly ordered items (M-R) for conventional survey format. Significant differences in item difficulty and item discrimination were found for two of the three scales. Differences in scale reliability were detected for the procrastination and …
