This work is directed towards developing flexible Bayesian statistical methods
in the semi- and nonparamteric regression modeling framework with special focus on
analyzing data from biological and genetic experiments. This dissertation attempts to
solve two such problems in this area. In the first part, we study penalized regression
splines (P-splines), which are low-order basis splines with a penalty to avoid under-
smoothing. Such P-splines are typically not spatially adaptive, and hence can have
trouble when functions are varying rapidly. We model the penalty parameter inherent
in the P-spline method as a heteroscedastic regression function. We develop a full
Bayesian hierarchical structure to do this and use Markov Chain Monte Carlo tech-
niques for drawing random samples from the posterior for inference. We show that
the approach achieves very competitive performance as compared to other methods.
The second part focuses on modeling DNA microarray data. Microarray technology
enables us to monitor the expression levels of thousands of genes simultaneously and
hence to obtain a better picture of the interactions between the genes. In order to
understand the biological structure underlying these gene interactions, we present a
hierarchical nonparametric Bayesian model based on Multivariate Adaptive Regres-sion Splines (MARS) to capture the functional relationship between genes and also
between genes and disease status. The novelty of the approach lies in the attempt to
capture the complex nonlinear dependencies between the genes which could otherwise
be missed by linear approaches. The Bayesian model is flexible enough to identify
significant genes of interest as well as model the functional relationships between the
genes. The effectiveness of the proposed methodology is illustrated on leukemia and
breast cancer datasets.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/4856 |
| Date | 25 April 2007 |
| Creators | Baladandayuthapani, Veerabhadran |
| Contributors | Carroll, Raymond J., Mallick, Bani K. |
| Publisher | Texas A&M University |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | 1199094 bytes, electronic, application/pdf, born digital |
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