baySeq: Empirical Bayesian analysis of patterns of differential expression in count data

This vignette is intended to give a rapid introduction to the commands used in implementing two methods of evaluating differential expression in Solexa-type, or count data by means of the baySeq R package. For fuller details on the methods being used, consult Hardcastle & Kelly [1]. The major improvement made in this release is the option to include region length in evaluating differential expression between genomic regions (e.g. genes). See Section 6.3.1 for more details. We assume that we have discrete data from a set of sequencing or other highthroughput experiments, arranged in a matrix such that each column describes a sample and each row describes some entity for which counts exist. For example, the rows may correspond to the different sequences observed in a sequencing experiment. The data then consists of the number of times each sequence is observed in each sample. We wish to determine which, if any, rows of the data correspond to some patterns of differential expression across the samples. This problem has been addressed for pairwise differential expression by the edgeR [3] package. However, baySeq takes an alternative approach to analysis that allows more complicated patterns of differential expression than simple pairwise comparison, and thus is able to cope with more complex experimental designs. We also observe that the methods implemented in baySeq perform at least as well, and in some circumstances considerably better than those implemented in edgeR [1]. baySeq uses empirical Bayesian methods to estimate the posterior likelihoods of each of a set of models that define patterns of differential expression for each row. This approach begins by considering a distribution for the row defined by a set of underlying parameters for which some prior distribution exists. By estimating this prior distribution from the data, we are able to assess, for a given model about the relatedness of our underlying parameters for multiple libraries, the posterior likelihood of the model. In forming a set of models upon the data, we consider which patterns are biologically likely to occur in the data. For example, suppose we have count data from some organism in condition A and condition B. Suppose further that we have two biological replicates for each condition, and hence four libraries A1, A2, B1, B2, where A1, A2 and B1, B2 are the replicates. It is reasonable to suppose that at least some of the rows may be unaffected by our experimental conditions A and B, and the count data for each sample in these rows will