Genomics GM_W0002

Title : SPARSITY MODELING FOR HIGH DIMENSIONALSYSTEMS: APPLICATIONS IN GENOMICS AND STRUCTURAL BIOLOGY
Author : Joseph Edward Lucas
Year : 2006
Place of publish :
Abstract :

 The availability of very high dimensional data has brought sparsity modeling to
the forefront of statistical research in recent years. From complex physical models
with hundreds of parameters to DNA microarrays which offer observations in
tens to hundreds of thousands of dimensions, separating relevant and irrelevant
parameters is becoming more and more important. This dissertation will focus
on innovations in the area of variable and model selection as they pertain to these
high dimensional systems.
Chapter 1 will discuss work from the literature on the areas of variable and
model selection.
Chapter 2 will describe an innovation to hierarchical variable selection modeling
that corrects errors that stem from assuming incorrectly that multiple thousands
of observations are informing about the same distribution.
In Chapter 3, we introduce a novel technique for applying variable selection
priors to induce sparsity in variance modeling.
One of the weaknesses of DNA microarrays is their sensitivity to the conditions
under which they were prepared. Chapter 4 describes a technique for correcting
the systematic bias that is introduced by these extreme sensitivities.
Chapters 5 and 6 are both case studies. They focus on implementing the
techniques described in chapters 2-4 in real world situations in order to ferret out
pathway signatures and to apply those to clinical situations.
Chapter 7 will introduce a new technique for sampling from a point mass
mixture prior when calculation of the conditional probability is impossible.
In Chapter 8, we apply this technique to a challenging problem in structural
biology.
For Chapter 9, we switch gears somewhat and apply some of the techniques
of decision theory the protein folding problem introduced in chapter 8. We are
able to use the results of our model fitting to inform future decisions for studying
polypeptide helicity.
Finally, we close, in Chapter 10, with some areas for future work that have
opened up as a result of studying these variable selection techniques.