Ya Su 
Postdoctoral Research Associate, Department of Statistics
Texas A&M University
Nonparametric Bayesian Deconvolution of a Symmetric Unimodal Density, with Application to Genomics
ABSTRACT
We consider nonparametric measurement error density deconvolution subject to het- eroscedastic measurement errors as well as symmetry about zero and shape constraints, in particular unimodality. The problem is motivated by genomics applications, where the observed data are estimated effect sizes from a regression on multiple genetic factors, as occurs in genome-wide association studies and in microarray applications. We exploit the fact that any symmetric and unimodal density can be expressed as a mixture of symmetric uniforms densities, and model the mixing density using a Dirichlet process location-mixture of Gamma distributions. We do the computations within a Bayesian context, describe a simple scalable implementation that is linear in the sample size, and show that the estimate of the unknown target density is consistent. Within our application context of regression effect sizes, the target density is likely to have a large probability near zero (the near null effects) coupled with a heavy-tailed distribution (the actual effects). Simulations show that unlike standard deconvolution methods, our Constrained Bayesian method does a much bet- ter job of reconstruction of the target density. An application to a genome-wide association study to predict height shows similar results.
Monday, 11/27/17, 12:30 PM, BLOC 521
