Abstract: Understanding the function of biological molecules requires statistical methods for assessing covariability across multiple dimensions as well as accounting for complex measurement error and missing data. In this talk, I will discuss two models for covariance estimation which have applications in molecular biology. In the first part of the talk, I will describe a model-based method for evaluating heterogeneity among several p x p covariance matrices in the large p, small n setting and will illustrate the utility of the method for exploratory analyses of high-dimensional multivariate gene expression data. In the second half of the talk, I will describe the role of covariance estimation in quantifying how cells regulate protein levels. Specifically, estimates of the correlation between steady-state levels of mRNA and protein are used to assess the degree to which protein levels are determined by post-transcriptional processes. Differences in cell preparation, measurement technology and protocol, as well as the pervasiveness of missing data complicate the accurate estimation of this correlation. To address these issues, I fit a Bayesian hierarchical model to a compendium of 58 data sets from multiple labs to infer a structured covariance matrix of measurements. I contextualize and contrast our results to conclusions drawn in previous studies.