Abstract

The concept of sparsity is more and more central to practical data analysis and inference with increasingly high-dimensional data. Gene expression genomics is a key example context. As part of a series of projects that has developed Bayesian methodology for large-scale regression, ANOVA, and latent factor models, we have extended traditional Bayesian “variable selection” priors and modelling ideas to new hierarchical sparsity priors that are providing substantial practical gains in addressing false discovery and isolating significant gene-specific parameters/effects in highly multivariate studies involving thousands of genes. We discuss and review these developments, in the contexts of multivariate regression, ANOVA, and latent factor models for multivariate gene expression data arising in either observational or designed experimental studies. The development includes the use of sparse regression components to provide gene-sample-specific normalisation/correction based on control and housekeeping factors, an important general issue and one that can be critical – and critically misleading if ignored – in many gene expression studies. Two rich data sets are used to provide context and illustration. The first data set arises from a gene expression experiment designed to investigate the transcriptional response – in terms of responsive gene subsets and their expression signatures – to interventions that upregulate a series of key oncogenes. The second data set is observational, breast cancer tumour-derived data evaluated utilising a sparse latent factor model to define and isolate factors underlying the hugely complex patterns of association in gene expression patterns. We also mention software that implements these and other models and methods in one comprehensive framework.