Bayesian change-point analysis in linear regression model with scale mixtures of normal distributions

In this thesis, we consider Bayesian inference on the detection of variance change-point models with scale mixtures of normal (for short SMN) distributions. This class of distributions is symmetric and thick-tailed and includes as special cases: Gaussian, Student-t, contaminated normal, and slash distributions. The proposed models provide greater flexibility to analyze a lot of practical data, which often show heavy-tail and may not satisfy the normal assumption. As to the Bayesian analysis, we specify some prior distributions for the unknown parameters in the variance change-point models with the SMN distributions. Due to the complexity of the joint posterior distribution, we propose an efficient Gibbs-type with Metropolis- Hastings sampling algorithm for posterior Bayesian inference. Thereafter, following the idea of [1], we consider the problems of the single and multiple change-point detections. The performance of the proposed procedures is illustrated and analyzed by simulation studies. A real application to the closing price data of U.S. stock market has been analyzed for illustrative purposes.

NON-CHROMATOGRAPHIC PURIFICATION OF SYNTHETIC BIO-OLIGOMERS

Synthetic oligonucleotides and peptides have found wide applications in industry and academic research labs. There are ~60 peptide drugs on the market and over 500 under development. The global annual sale of peptide drugs in 2010 was estimated to be $13 billion. There are three oligonucleotide-based drugs on market; among them, the FDA newly approved Kynamro was predicted to have a $100 million annual sale. The annual sale of oligonucleotides to academic labs was estimated to be $700 million. Both bio-oligomers are mostly synthesized on automated synthesizers using solid phase synthesis technology, in which nucleoside or amino acid monomers are added sequentially until the desired full-length sequence is reached. The additions cannot be complete, which generates truncated undesired failure sequences. For almost all applications, these impurities must be removed. The most widely used method is HPLC. However, the method is slow, expensive, labor-intensive, not amendable for automation, difficult to scale up, and unsuitable for high throughput purification. It needs large capital investment, and consumes large volumes of harmful solvents. The purification costs are estimated to be more than 50% of total production costs. Other methods for bio-oligomer purification also have drawbacks, and are less favored than HPLC for most applications. To overcome the problems of known biopolymer purification technologies, we have developed two non-chromatographic purification methods. They are (1) catching failure sequences by polymerization, and (2) catching full-length sequences by polymerization. In the first method, a polymerizable group is attached to the failure sequences of the bio-oligomers during automated synthesis; purification is achieved by simply polymerizing the failure sequences into an insoluble gel and extracting full-length sequences. In the second method, a polymerizable group is attached to the full-length sequences, which are then incorporated into a polymer; impurities are removed by washing, and pure product is cleaved from polymer. These methods do not need chromatography, and all drawbacks of HPLC no longer exist. Using them, purification is achieved by simple manipulations such as shaking and extraction. Therefore, they are suitable for large scale purification of oligonucleotide and peptide drugs, and also ideal for high throughput purification, which currently has a high demand for research projects involving total gene synthesis. The dissertation will present the details about the development of the techniques. Chapter 1 will make an introduction to oligodeoxynucleotides (ODNs), their synthesis and purification. Chapter 2 will describe the detailed studies of using the catching failure sequences by polymerization method to purify ODNs. Chapter 3 will describe the further optimization of the catching failure sequences by polymerization ODN purification technology to the level of practical use. Chapter 4 will present using the catching full-length sequence by polymerization method for ODN purification using acid-cleavable linker. Chapter 5 will make an introduction to peptides, their synthesis and purification. Chapter 6 will describe the studies using the catching full-length sequence by polymerization method for peptide purification.