This dissertation research consists of two topics, population stochastics approximation Monte Carlo (Pop-SAMC) for Baysian model selection problems and ChIP-chip data analysis. The following two paragraphs give a brief introduction to each of the two topics, respectively. Although the reversible jump MCMC (RJMCMC) has the ability to traverse the space of possible models in Bayesian model selection problems, it is prone to becoming trapped into local mode, when the model space is complex. SAMC, proposed by Liang, Liu and Carroll, essentially overcomes the difficulty in dimension-jumping moves, by introducing a self-adjusting mechanism. However, this learning mechanism has not yet reached its maximum efficiency. In this dissertation, we propose a Pop-SAMC algorithm; it works on population chains of SAMC, which can provide a more efficient self-adjusting mechanism and make use of crossover operator from genetic algorithms to further increase its efficiency. Under mild conditions, the convergence of this algorithm is proved. The effectiveness of Pop-SAMC in Bayesian model selection problems is examined through a change-point identification example and a large-p linear regression variable selection example. The numerical results indicate that Pop- SAMC outperforms both the single chain SAMC and RJMCMC significantly. In the ChIP-chip data analysis study, we developed two methodologies to identify the transcription factor binding sites: Bayesian latent model and population-based test. The former models the neighboring dependence of probes by introducing a latent indicator vector; The later provides a nonparametric method for evaluation of test scores in a multiple hypothesis test by making use of population information of samples. Both methods are applied to real and simulated datasets. The numerical results indicate the Bayesian latent model can outperform the existing methods, especially when the data contain outliers, and the use of population information can significantly improve the power of multiple hypothesis tests.

Biological processes in living organisms consist of a vast number of different molecular networks and interactions, which are complex and often hidden from our understanding. This work is focused on recovery of such details for two quite distant examples: acclimation to extreme freezing tolerance in Siberian spruce (Picea obovata) and detection of proteins associated with prostate cancer. The first biological system in the study, upon P. obovata, is interesting by this species ability to adapt and sustain extremely low temperatures, such as -60⁰C or below. Despite decades of investigations, the essential features and mechanisms of the amazing ability of this species still remains unclear. To enhance knowledge about extreme freezing tolerance, the metabolome and proteome of P. obovata’s needles were collected during the tree’s acclimation period, ranging from mid August to January, and have been analyzed. The second system within this study is the plasma proteome analysis of high risk prostate cancer (PCa) patients, with and without bone metastases. PCa is one of the most common cancers among Swedish men, which can abruptly develop into an aggressive, lethal disease. The diagnostic tools, including PSA-tests, are insufficient in predicting the disease’s aggressiveness and novel prognostic markers are urgently required. Both biological systems have been analyzed following similar steps: by two-dimensional difference gel electrophoresis (2D-DIGE) techniques, followed by protein identification using mass spectrometry (MS) analysis and multivariate methods. Data processing has been utilized for searching for proteins that serve as unique indicators for characterizing the status of the systems. In addition, the gas chromatography-mass spectrometry (GC-MS) study of the metabolic content of P.obovata’s needles, from the extended observation period, has been performed. The studies of both systems, combined with thorough statistical analysis of experimental outcomes, have resulted in novel insights and features for both P. obovata and prostate cancer. In particular, it has been shown that dehydrins, Hsp70s, AAA+ ATPases, lipocalin and several proteins involved in cellular metabolism etc., can be uniquely associated with acclimation to extreme freezing in conifers. Metabolomic analysis of P. obovata needles has revealed systematic metabolic changes in carbohydrate and lipid metabolism. Substantial increase of raffinose, accumulation of desaturated fatty acids, sugar acids, sugar alcohols, amino acids and polyamines that may act as compatible solutes or cryoprotectants have all been observed during the acclimation process. Relevant proteins for prostate cancer progression and aggressiveness have been identified in the plasma proteome study, for patients with and without bone metastasis. Proteins associated with lipid transport, coagulation, inflammation and immune response have been found among them.