Abstract

Multivariate regression models with many responses has attracted the attention of the statistical community in very recent years. A notable example is the paradigm of eQTL analysis, where thousands of transcripts are regressed versus (hundred of) thousands of markers. In this context the usual problem of multimodality of the posterior distribution, when p>>n, is further exacerbated by the dimension of the response matrix, usually q>>n. The problem can be even more complex when transcriptomic data are available for multiple tissues, introducing a third dimension in the response matrix.

In this talk we introduce a new searching algorithm called Hierarchical Evolutionary Stochastic Search (HESS) where the responses are linked in a hierarchical way. To reduce the computational burden, most of the regression parameters are integrated out. A novel sampling strategy based on Evolutionary Monte Carlo has been designed to efficiently sample from the huge parametric space. Moreover the whole set of past visited models are also considered through an adaptive proposal distribution, allowing the algorithm to balance between the freedom of exploration and the ability to persist on models in regions of high posterior probability.

Simulated and real data sets are analysed to demonstrate the performance of the proposed algorithm when p and q are both larger than n and when multiple tissues are considered. Collaborators on various aspects of work: Sylvia Richardson, David Welsh and Enrico Petretto.