The specific objectives of this project are to: (i) develop statistical models, Bayesian methodology, and computational methods for discovery of gene regulatory networks, ii) develop a class of hierarchical models for phylogenetic inference in the presence of fragmentary sequence alignments, iii) develop new classes of models and computational methods for expression trait loci detection, iv) develop Bayesian joint semiparametric models for analyzing cDNA gene expression data and time-to-event data, and v) examine Bayesian hierarchical models and gene selection algorithms for analyzing time course microarray data. In i) we develop a novel mixture of hierarchical regression models to simultaneously address the issue of unknown clusters of co-regulated genes, and the effect of a set of transcription factors regulating a gene cluster. For ii), we develop a hierarchical model for phylogenetic tree construction from fragmentary sequence alignment data. Our development of the model accommodates arbitrary sequence lengths and fragments. In fitting the model, we devise a profile likelihood approach that leads to closed form estimates of the parameters of interest. Various extensions of the model are also proposed. For iii), we will develop a model to model the prior probabilities of a transcript mapping to a marker in terms of the transcript's genomic proximity to the marker. We use a log-linear model, called the Proximity Model, for the mixture probabilities that contains the Mixture Over Marker (MOM) model as a special case. For iv) we propose a model that accounts for the effects measurement error in cDNA microarray experiments has on the assessment of associations between gene expression and time-to-event data. We propose a Bayesian hierarchical latent variable model linked to a piecewise constant proportional hazards model for the time-to- event data. For v), we use a log-normal random effects model for the gene expression measurements over time to characterize the temporal patterns of gene expression in each biological condition. We consider a class of priors to induce correlation structures between genes. We also propose a gene selection algorithm, using a ratio-based parameter, to identify genes that have different patterns of expression among biological conditions, in response to time and other important experimental factors. ? ? ?
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