Date on Master's Thesis/Doctoral Dissertation


Document Type

Doctoral Dissertation

Degree Name

Ph. D.



Degree Program

Applied and Industrial Mathematics, PhD

Committee Chair

Gill, Ryan

Committee Co-Chair (if applicable)

Li, Jiaxu

Committee Member

Li, Jiaxu

Committee Member

Mitra, Riten

Committee Member

Sahoo, Prasanna

Committee Member

Tone, Cristina

Author's Keywords

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.

Included in

Biostatistics Commons