Browsing by Subject "ChIP-chip"
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Item Population SAMC, ChIP-chip Data Analysis and Beyond(2011-02-22) Wu, MingqiThis 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.Item Topics in multiple hypotheses testing(Texas A&M University, 2007-04-25) Qian, YiIt is common to test many hypotheses simultaneously in the application of statistics. The probability of making a false discovery grows with the number of statistical tests performed. When all the null hypotheses are true, and the test statistics are indepen- dent and continuous, the error rates from the family wise error rate (FWER)- and the false discovery rate (FDR)-controlling procedures are equal to the nominal level. When some of the null hypotheses are not true, both procedures are conservative. In the first part of this study, we review the background of the problem and propose methods to estimate the number of true null hypotheses. The estimates can be used in FWER- and FDR-controlling procedures with a consequent increase in power. We conduct simulation studies and apply the estimation methods to data sets with bio- logical or clinical significance. In the second part of the study, we propose a mixture model approach for the analysis of ChIP-chip high density oligonucleotide array data to study the interac- tions between proteins and DNA. If we could identify the specific locations where proteins interact with DNA, we could increase our understanding of many important cellular events. Most experiments to date are performed in culture on cell lines, bac- teria, or yeast, and future experiments will include those in developing tissues, organs, or cancer biopsies, and they are critical in understanding the function of genes and proteins. Here we investigate the ChIP-chip data structure and use a beta-mixture model to help identify the binding sites. To determine the appropriate number of components in the mixture model, we suggest the Anderson-Darling testing. Our study indicates that it is a reasonable means of choosing the number of components in a beta-mixture model. The mixture model procedure has broad applications in biology and is illustrated with several data sets from bioinformatics experiments.