Digitized by Kansas Correctional Industries

Digitized by Kansas Correctional Industries

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Least squares linear regression is a common tool in ecological research. One of the central assumptions of least squares linear regression is that the independent variable is measured without error. But this variable is measured with error whenever it is a sample mean. The significance of such contraventions is not regularly assessed in ecological studies. A simulation program was made to provide such an assessment. The program requires a hypothetical data set, and using estimates of S$ sp2$ it scatters the hypothetical data to simulate the effect of sampling error. A regression line is drawn through the scattered data, and SSE and r$ sp2$ are measured. This is repeated numerous times (e.g. 1000) to generate probability distributions for r$ sp2$ and SSE. From these distributions it is possible to assess the likelihood of the hypothetical data resulting in a given SSE or r$ sp2$. The method was applied to survey data used in a published TP-CHLa regression (Pace 1984). Beginning with a hypothetical, linear data set (r$ sp2$ = 1), simulated scatter due to sampling exceeded the SSE from the regression through the survey data about 30% of the time. Thus chances are 3 out of 10 that the level of uncertainty found in the surveyed TP-CHLa relationship would be observed if the true relationship were perfectly linear. If this is so, more precise and more comprehensive models will only be possible when better estimates of the means are available. This simulation approach should apply to all least squares regression studies that use sampled means, and should be especially relevant to studies that use log-transformed values.

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Indiana University-Purdue University Indianapolis (IUPUI) / The objective of this thesis is to compare automated methods for performing analysis of flow cytometry data. Flow cytometry is an important and efficient tool for analyzing the characteristics of cells. It is used in several fields, including immunology, pathology, marine biology, and molecular biology. Flow cytometry measures light scatter from cells and fluorescent emission from dyes which are attached to cells. There are two main tasks that must be performed. The first is the adjustment of measured fluorescence from the cells to correct for the overlap of the spectra of the fluorescent markers used to characterize a cell’s chemical characteristics. The second is to use the amount of markers present in each cell to identify its phenotype. Several methods are compared to perform these tasks. The Unconstrained Least Squares, Orthogonal Subspace Projection, Fully Constrained Least Squares and Fully Constrained One Norm methods are used to perform compensation and compared. The fully constrained least squares method of compensation gives the overall best results in terms of accuracy and running time. Spectral Clustering, Gaussian Mixture Modeling, Naive Bayes classification, Support Vector Machine and Expectation Maximization using a gaussian mixture model are used to classify cells based on the amounts of dyes present in each cell. The generative models created by the Naive Bayes and Gaussian mixture modeling methods performed classification of cells most accurately. These supervised methods may be the most useful when online classification is necessary, such as in cell sorting applications of flow cytometers. Unsupervised methods may be used to completely replace manual analysis when no training data is given. Expectation Maximization combined with a cluster merging post-processing step gives the best results of the unsupervised methods considered.