High-throughput genomic data contain gazillion of information that are influenced by the complex biological processes in the cell. As such, appropriate mathematical modeling frameworks are required to understand the data and the data generating processes. This dissertation focuses on the formulation of mathematical models and the description of appropriate computational algorithms to obtain insights from genomic data. Specifically, characterization of intra-tumor heterogeneity is studied. Based on the total number of allele copies at the genomic locations in the tumor subclones, the problem is viewed from two perspectives: the presence or absence of copy-neutrality assumption. With the presence of copy-neutrality, it is assumed that the genome contains mutational variability and the three possible genotypes may be present at each genomic location. As such, the genotypes of all the genomic locations in the tumor subclones are modeled by a ternary matrix. In the second case, in addition to mutational variability, it is assumed that the genomic locations may be affected by structural variabilities such as copy number variation (CNV). Thus, the genotypes are modeled with a pair of (Q + 1)-ary matrices. Using the categorical Indian buffet process (cIBP), state-space modeling framework is employed in describing the two processes and the sequential Monte Carlo (SMC) methods for dynamic models are applied to perform inference on important model parameters. Moreover, the problem of estimating gene regulatory network (GRN) from measurement with missing values is presented. Specifically, gene expression time series data may contain missing values for entire expression values of a single point or some set of consecutive time points. However, complete data is often needed to make inference on the underlying GRN. Using the missing measurement, a dynamic stochastic model is used to describe the evolution of gene expression and point-based Gaussian approximation (PBGA) filters with one-step or two-step missing measurements are applied for the inference. Finally, the problem of deconvolving gene expression data from complex heterogeneous biological samples is examined, where the observed data are a mixture of different cell types. A statistical description of the problem is used and the SMC method for static models is applied to estimate the cell-type specific expressions and the cell type proportions in the heterogeneous samples.

Indiana University-Purdue University Indianapolis (IUPUI) / This thesis is aimed at creating a pipeline for analyzing DNA methylation epigenetics data and creating a data model structured well enough to store the analysis results of the pipeline. In addition to storing the results, the model is also designed to hold information which will help researchers to decipher a meaningful epigenetics sense from the results made available. Current major epigenetics resources such as PubMeth, MethyCancer, MethDB and NCBI’s Epigenomics database fail to provide holistic view of epigenetics. They provide datasets produced from different analysis techniques which raises an important issue of data integration. The resources also fail to include numerous factors defining the epigenetic nature of a gene. Some of the resources are also struggling to keep the data stored in their databases up-to-date. This has diminished their validity and coverage of epigenetics data. In this thesis we have tackled a major branch of epigenetics: DNA methylation. As a case study to prove the effectiveness of our pipeline, we have used stage-wise DNA methylation and expression raw data for Lung adenocarcinoma (LUAD) from TCGA data repository. The pipeline helped us to identify progressive methylation patterns across different stages of LUAD. It also identified some key targets which have a potential for being a drug target. Along with the results from methylation data analysis pipeline we combined data from various online data reserves such as KEGG database, GO database, UCSC database and BioGRID database which helped us to overcome the shortcomings of existing data collections and present a resource as complete solution for studying DNA methylation epigenetics data.