A Bayesian hierarchical sparse factor model for estimating simultaneous covariance matrices for gestational outcomes in consecutive pregnancies.

Covariance estimation for multiple groups is a key feature for drawing inference from a heterogeneous population. One should seek to share information about common features in the dependence structures across the various groups. In this paper, we introduce a novel approach for estimating the covariance matrices for multiple groups using a hierarchical latent factor model that shrinks the factor loadings across groups toward a global value. Using a sparse spike and slab model on these loading coefficients allows for a sparse formulation of our model. Parameter estimation is accomplished through a Markov chain Monte Carlo scheme, and a model selection approach is used to select the number of factors to use. We validate our model through extensive simulation studies. Finally, we apply our methodology to the NICHD Consecutive Pregnancies Study to estimate the correlations between birth weights and gestational ages of three consecutive birth within four different subgroups (underweight, normal, overweight, and obese) of women.

A continuous-index Bayesian hidden Markov model for prediction of nucleosome positioning in genomic DNA.

Nucleosomes are units of chromatin structure, consisting of DNA sequence wrapped around proteins called "histones." Nucleosomes occur at variable intervals throughout genomic DNA and prevent transcription factor (TF) binding by blocking TF access to the DNA. A map of nucleosomal locations would enable researchers to detect TF binding sites with greater efficiency. Our objective is to construct an accurate genomic map of nucleosome-free regions (NFRs) based on data from high-throughput genomic tiling arrays in yeast. These high-volume data typically have a complex structure in the form of dependence on neighboring probes as well as underlying DNA sequence, variable-sized gaps, and missing data. We propose a novel continuous-index model appropriate for non-equispaced tiling array data that simultaneously incorporates DNA sequence features relevant to nucleosome formation. Simulation studies and an application to a yeast nucleosomal assay demonstrate the advantages of using the new modeling framework, as well as its robustness to distributional misspecifications. Our results reinforce the previous biological hypothesis that higher-order nucleotide combinations are important in distinguishing nucleosomal regions from NFRs.