Date on Master's Thesis/Doctoral Dissertation
Applied and Industrial Mathematics, PhD
Committee Co-Chair (if applicable)
maximum likelihood estmates; copy number variation; circular binary segmentation; negative binomial distribution; Newton-Raphson method; poisson distribution
A Copy Number Variation (CNV) detection problem is considered using Circular Binary Segmentation (CBS) procedures, including newly developed procedures based on likelihood ratio tests with the parametric bootstrap for models based on discrete distributions for count data (Poisson and negative binomial) and a widely-used DNAcopy package. Results from the literature concerning maximum likelihood estimation for the negative binomial distribution are reviewed. The Newton-Raphson method is used to find the root of the derivative of the profile log likelihood function when applicable, and it is proven that this method converges to the true Maximum Likeihood Estimate (MLE), if the starting point for the Newton-Raphson is selected appropriately and the MLE exists.
Bandara, Udika Iroshini, "Likelihood-based methods for analysis of copy number variation using next generation sequencing data." (2017). Electronic Theses and Dissertations. Paper 2778.