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Parameter estimation for outlier corrupted data.
München, Technische Universität, Mathematische Fakultät, Master-Thesis, 2016, 61 S.
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Mathematical models are a valuable tool to answer biological questions or evaluate competing hypotheses which are not within reach of experiments. Since commonly not all system parameters are known, models need to be calibrated based on experimental data. However, outlier corrupted data poses a serious threat to model alibration as outliers may lead to distorted parameters, which result in wrong model predictions. Detecting and removing those outliers is a challenging task with regard to the complexity and amount of biological data. A reasonable alternative approach constitutes robust parameter estimation. For parameter estimation it is commonly assumed that the deviation of the measurement from the predicted observable is normally distributed. This assumption is, however, strongly aected by large erroneous measurements. Heavier-tailed distributions, that have heavier tails than the normal distribution, are less susceptible to outliers and consequently, using a heavier-tailed distribution as distribution assumption for the deviation of the measurements from the predicted observables yields a robust approach to parameter estimation. In the presented methods for estimating the parameters of ordinary dierential equation (ODE) models, we propose the Laplace, Cauchy and Student's t distribution as heaviertailed alternatives to the normal distribution assumption. The robustness of our novel methods was assessed for population average data, which was modied according to dened outlier scenarios. At rst articially generated data of a conversion reaction was studied and the results showed that the new methods are able to decrease the error of parameter estimates for outlier corrupted data. To support this nding an application study to articially perturbed experimental data of the Jak/Stat signaling pathway was performed. Using heavier-tailed distribution assumptions constitutes indeed a robust approach to parameter estimatio for outlier corrupted data that leads to reliable parameter estimates. Since model accuracy is a prerequisite for reliable predictions of the behavior of a biological process, the proposed methods will enhance the investigation of biological systems.
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Publication type Other: Thesis
Thesis type Master thesis
Quellenangaben Pages: 61 S.
University Technische Universität
University place München
Faculty Mathematische Fakultät
Institute(s) Institute of Computational Biology (ICB)