Regression models describingthe dependence between a univariate response and a set of covariates play a fundamental role in statistics. In the last two decades, a tremendous effort has been made in developing flexible regression techniques such as generalized additive models(GAMs) with the aim of modelling the expected value of a response variable as a sum of smooth unspecified functions of predictors. Many nonparametric regression methodologies exist includinglocal-weighted regressionand smoothing splines. Here the focus is on penalized regression spline methods which can be viewed as a generalization of smoothing splines with a more flexible choice of bases and penalties. This thesis addresses three issues. First, the problem of model misspecification is treated by extending the instrumental variable approach to the GAM context. Second, we study the theoretical and empirical properties of the confidence intervals for the smooth component functions of a GAM. Third, we consider the problem of variable selection within this flexible class of models. All results are supported by theoretical arguments and extensive simulation experiments which shed light on the practical performance of the methods discussed in this thesis.

Typescript (photocopy). / Digitized by Kansas Correctional Industries

This study consists of the sensitivity analysis for two previously developed tumor growth models: Gompertz model and quotient model. The two models are considered in both continuous and discrete time. In continuous time, model parameters are estimated using least-square method, while in discrete time, the partial-sum method is used. Moreover, frequentist and Bayesian methods are used to construct confidence intervals and credible intervals for the model parameters. We apply the Markov Chain Monte Carlo (MCMC) techniques with the Random Walk Metropolis algorithm with Non-informative Prior and the Delayed Rejection Adoptive Metropolis (DRAM) algorithm to construct parameters' posterior distributions and then obtain credible intervals.

In this dissertation, we study several problems related to intervals and develop efficient algorithms for them. Interval problems have many applications in reality because many objects, values, and ranges are intervals in nature, such as time intervals, distances, line segments, probabilities, etc. Problems on intervals are gaining attention also because intervals are among the most basic geometric objects, and for the same reason, computational geometry techniques find useful for attacking these problems. Specifically, the problems we study in this dissertation includes the following: balanced splitting on weighted intervals, minimizing the movements of spreading points, dispersing points on intervals, multiple barrier coverage, and separating overlapped intervals on a line. We develop efficient algorithms for these problems and our results are either first known solutions or improve the previous work. In the problem of balanced splitting on weighted intervals, we are given a set of n intervals with non-negative weights on a line and an integer k ≥ 1. The goal is to find k points to partition the line into k + 1 segments, such that the maximum sum of the interval weights in these segments is minimized. We give an algorithm that solves the problem in O(n log n) time. Our second problem is on minimizing the movements of spreading points. In this problem, we are given a set of points on a line and we want to spread the points on the line so that the minimum pairwise distance of all points is no smaller than a given value δ. The objective is to minimize the maximum moving distance of all points. We solve the problem in O(n) time. We also solve the cycle version of the problem in linear time. For the third problem, we are given a set of n non-overlapping intervals on a line and we want to place a point on each interval so that the minimum pairwise distance of all points are maximized. We present an O(n) time algorithm for the problem. We also solve its cycle version in O(n) time. The fourth problem is on multiple barrier coverage, where we are given n sensors in the plane and m barriers (represented by intervals) on a line. The goal is to move the sensors onto the line to cover all the barriers such that the maximum moving distance of all sensors is minimized. Our algorithm for the problem runs in O(n2 log n log log n + nm log m) time. In a special case where the sensors are all initially on the line, our algorithm runs in O((n + m) log(n + m)) time. Finally, for the problem of separating overlapped intervals, we have a set of n intervals (possibly overlapped) on a line and we want to move them along the line so that no two intervals properly intersect. The objective is to minimize the maximum moving distance of all intervals. We propose an O(n log n) time algorithm for the problem. The algorithms and techniques developed in this dissertation are quite basic and fundamental, so they might be useful for solving other related problems on intervals as well.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 135-139).

The purpose of the study was to develop a sequential test method for obtaining a confidence interval in life-testing. The problem of using a maximum likelihood estimator based upon grouped data was considered. Life-times that were investigated are described by the exponential distribution. The sequential test used the length of the confidence interval as a stopping rule.The test method and necessary calculations were described. The results of using different length values as a stopping rule were compared using a computer simulation. Results are indicated in two categories: percent of time the estimate contained the true parameter value, and average number of data collection times needed to obtain the estimate. It was concluded that the test method was accurate and efficient. The length value was a considerable factor in deriving good results from the test method. It was recommended that research be continued to establish a method of choosing the best length value to be used.Ball State UniversityMuncie, IN 47306

El objetivo de la presente tesis es desarrollar un nuevo método de generación de umbrales adaptativos mediante la obtención de las respuestas temporales máxima y mínima a cada instante de tiempo, denominadas envolventes, a partir del modelo de un sistema con incertidumbre parmétrica de tipo intercalar en los parámetros. El nuevo algoritmo para la generación de envolventes presentado en esta tesis está basado en una ventana temporal deslizante y optimización. Una vez obtenidas las envolventes a partir del nuevo algoritmo de generación, se utilizarán para la detección robusta de fallos en procesos industriales.La generación de envolventes para su posterior utilización como un umbral adaptativo en un método de detección y diagnóstico de fallo es todavía hoy un problema abierto. Se han propuesto muchos algoritmos para su generación pero ninguno de ellos consiguegarantizar la obtención de las envolventes correctas, entendiendo como correctas aquellas envolventes debidas a la incertidumbre presente en los parámetros del sistema y a la incertidumbre sobre los estados iniciales.El método de generación de envolventes propuesto en esta tesis consigue generar las envolventes con la precisión deseada y con la incertidumbre acumulada por el proceso de generación de las envolventes acotada.Los resultados y aportaciones más significativas que se han obtenido en esta tesis se enumeran a continuación:. Nuevo algoritmo para la generación de envolventes basado en optimización y en el paradigma de las ventanas deslizantes.. Determinación analítica y mediante simulaciones de la longitud de ventana óptima para obtener unas envolventes correctas.. Demostración de que el nuevo algoritmo evita los problemas que padecen la mayoría de algoritmos de generación de envolventes: wrapping, multiincidencias, problemas de óptimos locales y el problema de propagación de la incertidumbre.

Nearly every decision must be made with a degree of uncertainty regarding the outcome. Decision making based on modeling and simulation predictions needs to incorporate and aggregate uncertain evidence. To validate multiscale simulation models, it may be necessary to consider evidence collected at a length scale that is different from the one at which a model predicts. In addition, traditional methods of uncertainty analysis do not distinguish between two types of uncertainty: uncertainty due to inherently random inputs, and uncertainty due to lack of information about the inputs. This thesis examines and applies a Bayesian approach for model parameter validation that uses generalized interval probability to separate these two types of uncertainty. A generalized interval Bayes’ rule (GIBR) is used to combine the evidence and update belief in the validity of parameters. The sensitivity of completeness and soundness for interval range estimation in GIBR is investigated. Several approaches to represent complete ignorance of probabilities’ values are tested. The result from the GIBR method is verified using Monte Carlo simulations. The method is first applied to validate the parameter set for a molecular dynamics simulation of defect formation due to radiation. Evidence is supplied by the comparison with physical experiments. Because the simulation includes variables whose effects are not directly observable, an expanded form of GIBR is implemented to incorporate the uncertainty associated with measurement in belief update. In a second example, the proposed method is applied to combining the evidence from two models of crystal plasticity at different length scales.

During sustained voluntary contractions, the variability in motor unit interspike intervals increases with fatigue. This increase in variability may represent an adaptive mechanism to prevent fatigue. We investigated whether randomly modulating interpulse intervals (IPI) in a constant frequency stimulation protocol reduces force loss over time compared to a non-modulated constant frequency protocol. A second purpose of this study was to investigate the role of the M-wave in force generation during evoked contractions. Eight healthy subjects participated in three 3-minute fatigue protocols of the thenar muscles elicited by supramaximal stimulation of the median nerve. All three protocols had a mean IPI of 33.3ms and only differed in the type of modulation. One protocol consisted of 0% modulation ('Constant'), another protocol consisted of uniformly distributed modulation of [plus or minus]20% ('Variable'), and a third protocol consisted of ramped modulation from 0 to [plus or minus]20% ('Ramp'). There was no significant difference between overall force-time integrals for the three protocols. There was a significant reduction in M-wave amplitude for all three protocols; however, the M-wave immediately following the 'Ramp' protocol was significantly larger than the M-wave immediately following the 'Constant' protocol. We conclude that modulation is ineffective at preserving force output and somewhat effective at preserving the M-wave amplitude. The varied reductions in fatigued M-waves suggest that it is not necessarily a limiting factor in force output and that it was not necessarily linked to the force loss in this experiment. / text

The mean residual life (MRL) function is an important function in survival analysis, actuarial science, economics and other social sciences and reliability for characterizing lifetime. Different methods have been proposed for doing inference on the MRL but their coverage probabilities for small sample sizes are not good enough. In this thesis we apply the empirical likelihood method and carry out a simulation study of the MRL function using different statistical distributions. The simulation study does a comparison of the empirical likelihood method and the normal approximation method. The comparisons are based on the average lengths of confidence intervals and coverage probabilities. We also did comparisons based on median lengths of confidence intervals for the MRL. We found that the empirical likelihood method gives better coverage probability and shorter confidence intervals than the normal approximation method for almost all the distributions that we considered. Applying the two methods to real data we also found that the empirical likelihood method gives thinner pointwise confidence bands.