Power Conjugate Multilevel Models with Applications to Genomics

In the simultaneous estimation of a large number of related quantities, multilevel models provide a formal mechanism for effciently making use of the ensemble of information for deriving individual estimates. In this article we present a novel and flexible class of normal multilevel models, referred to as the "power conjugate family". This family overcomes some of the severe restrictions posed by standard conjugate normal models in describing the relationship between sources of variations at different levels of the model, while retaining attractive properties from the point of view of computations. We show that estimates based on this generalized family of conjugate distributions, outperform currently prevalent methods in a range of plausible simulated experiments. Our work was motivated by the analysis of data from high-throughput experiments in genomics. We illustrate the use of the power conjugate family on two such data sets, one of which gives an example where uncritical application of standard conjugate models can produce poor results.