Bayesian variable selection in structured high-dimensional covariate spaces with applications in genomics

We consider the problem of variable selection in regression modeling in high-dimensional spaces where there is known structure among the covariates. This is an unconventional variable selection problem for two reasons: (1) The dimension of the covariate space is comparable, and often much larger, than the number of subjects in the study, and (2) the covariate space is highly structured, and in some cases it is desirable to incorporate this structural information in to the model building process. We approach this problem through the Bayesian variable selection framework, where we assume that the covariates lie on an undirected graph and formulate an Ising prior on the model space for incorporating structural information. Certain computational and statistical problems arise that are unique to such high-dimensional, structured settings, the most interesting being the phenomenon of phase transitions. We propose theoretical and computational schemes to mitigate these problems. We illustrate our methods on two different graph structures: the linear chain and the regular graph of degree k. Finally, we use our methods to study a specific application in genomics: the modeling of transcription factor binding sites in DNA sequences. © 2010 American Statistical Association.

Genome-wide association study of Lp-PLA(2) activity and mass in the Framingham Heart Study.

Lipoprotein-associated phospholipase A(2) (Lp-PLA(2)) is an emerging risk factor and therapeutic target for cardiovascular disease. The activity and mass of this enzyme are heritable traits, but major genetic determinants have not been explored in a systematic, genome-wide fashion. We carried out a genome-wide association study of Lp-PLA(2) activity and mass in 6,668 Caucasian subjects from the population-based Framingham Heart Study. Clinical data and genotypes from the Affymetrix 550K SNP array were obtained from the open-access Framingham SHARe project. Each polymorphism that passed quality control was tested for associations with Lp-PLA(2) activity and mass using linear mixed models implemented in the R statistical package, accounting for familial correlations, and controlling for age, sex, smoking, lipid-lowering-medication use, and cohort. For Lp-PLA(2) activity, polymorphisms at four independent loci reached genome-wide significance, including the APOE/APOC1 region on chromosome 19 (p = 6 x 10(-24)); CELSR2/PSRC1 on chromosome 1 (p = 3 x 10(-15)); SCARB1 on chromosome 12 (p = 1x10(-8)) and ZNF259/BUD13 in the APOA5/APOA1 gene region on chromosome 11 (p = 4 x 10(-8)). All of these remained significant after accounting for associations with LDL cholesterol, HDL cholesterol, or triglycerides. For Lp-PLA(2) mass, 12 SNPs achieved genome-wide significance, all clustering in a region on chromosome 6p12.3 near the PLA2G7 gene. Our analyses demonstrate that genetic polymorphisms may contribute to inter-individual variation in Lp-PLA(2) activity and mass.

Spaces of Order: An African Poetics of Space

“Spaces of Order” argues that the African novel should be studied as a revolutionary form characterized by aesthetic innovations that are not comprehensible in terms of the novel’s European archive of forms. It does this by mapping an African spatial order that undermines the spatial problematic at the formal and ideological core of the novel—the split between a private, subjective interior, and an abstract, impersonal outside. The project opens with an examination of spatial fragmentation as figured in the “endless forest” of Amos Tutuola’s The Palmwine Drinkard (1952). The second chapter studies Chinua Achebe’s Things Fall Apart (1958) as a fictional world built around a peculiar category of space, the “evil forest,” which constitutes an African principle of order and modality of power. Chapter three returns to Tutuola via Ben Okri’s The Famished Road (1991) and shows how the dispersal of fragmentary spaces of exclusion and terror within the colonial African city helps us conceive of political imaginaries outside the nation and other forms of liberal political communities. The fourth chapter shows Nnedi Okorafor—in her 2014 science-fiction novel Lagoon—rewriting Things Fall Apart as an alien-encounter narrative in which Africa is center-stage of a planetary, multi-species drama. Spaces of Order is a study of the African novel as a new logic of world making altogether.

Analytic Torsion, the Eta Invariant, and Closed Differential Forms on Spaces of Metrics

The central idea of this dissertation is to interpret certain invariants constructed from Laplace spectral data on a compact Riemannian manifold as regularized integrals of closed differential forms on the space of Riemannian metrics, or more generally on a space of metrics on a vector bundle. We apply this idea to both the Ray-Singer analytic torsion

and the eta invariant, explaining their dependence on the metric used to define them with a Stokes' theorem argument. We also introduce analytic multi-torsion, a generalization of analytic torsion, in the context of certain manifolds with local product structure; we prove that it is metric independent in a suitable sense.