  Analysis of multivariate data sets from e.g. microarray studies frequently
results in lists of genes which are associated with some response of interest.
The biological interpretation is often complicated by the statistical
instability of the obtained gene lists with respect to sampling variations,
which may partly be due to the functional redundancy among genes, implying that
multiple genes can play exchangeable roles in the cell. In this paper we use
the concept of exchangeability of random variables to model this functional
redundancy and thereby account for the instability attributable to sampling
variations. We present a flexible framework to incorporate the exchangeability
into the representation of lists. The proposed framework supports
straightforward robust comparison between any two lists. It can also be used to
generate new, more stable gene rankings incorporating more information from the
experimental data. Using a microarray data set from lung cancer patients we
show that the proposed method provides more robust gene rankings than existing
methods with respect to sampling variations, without compromising the
biological significance.
