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Grobner Bases And Ideals Of Points, Eun R. Chang
Grobner Bases And Ideals Of Points, Eun R. Chang
Theses and Dissertations
The main point of this thesis is an introduction to the theory of Grobner bases. The concept of Grobner basis and construction of the Grobner basis by Buchberger's Algorithm, in which the notion of S-polynomials is introduced, and a few modified or improved versions of Grobner basis algorithm are reviewed in this paper. In Chapter 1, we have a review of ideals, the definitions and types of monomial ordering, the multivariate polynomial division algorithm and its examples. After ascertaining the monomial ordering on multivariate polynomials, we establish a leading term of a polynomial.In Chapter 2, after defining Grobner bases, we …
A Comparison For Longitudinal Data Missing Due To Truncation, Rong Liu
A Comparison For Longitudinal Data Missing Due To Truncation, Rong Liu
Theses and Dissertations
Many longitudinal clinical studies suffer from patient dropout. Often the dropout is nonignorable and the missing mechanism needs to be incorporated in the analysis. The methods handling missing data make various assumptions about the missing mechanism, and their utility in practice depends on whether these assumptions apply in a specific application. Ramakrishnan and Wang (2005) proposed a method (MDT) to handle nonignorable missing data, where missing is due to the observations exceeding an unobserved threshold. Assuming that the observations arise from a truncated normal distribution, they suggested an EM algorithm to simplify the estimation.In this dissertation the EM algorithm is …
Quantifying The Effects Of Correlated Covariates On Variable Importance Estimates From Random Forests, Ryan Vincent Kimes
Quantifying The Effects Of Correlated Covariates On Variable Importance Estimates From Random Forests, Ryan Vincent Kimes
Theses and Dissertations
Recent advances in computing technology have lead to the development of algorithmic modeling techniques. These methods can be used to analyze data which are difficult to analyze using traditional statistical models. This study examined the effectiveness of variable importance estimates from the random forest algorithm in identifying the true predictor among a large number of candidate predictors. A simulation study was conducted using twenty different levels of association among the independent variables and seven different levels of association between the true predictor and the response. We conclude that the random forest method is an effective classification tool when the goals …