Bayesian Modeling of Genome-Scale Phenomena

Genome-wide transcript quantification is commonly used for studying cellular responses to different experimental conditions or disease.  Each gene can potentially exhibit differential expression (change in the average number of transcription events) and/or differential splicing (change in the fractions of isoforms).   Commonly-used multiple-testing correction methods will reduce the significance of findings, and the more measurements are performed, the more severe the reduction will be.  This is true even if the alternative hypothesis is always correct, and it contradicts the idea that more experiments generate more knowledge.

We introduced a Bayesian approach to multiple comparisons that does not reduce the significance of tests if the proportion of true H1 remains the same.  That is, as long as experiments are designed in a reasonable manner, more experiments will increase knowledge.

The Posterior Error Probability (PEP) is the probability of no-effect - that either the expression of a gene does not change, or that the proportions of its isoforms remain the same between case and control samples.  Given a joint model of gene expression and alternative splicing, and measurements for a large number of genes and their isoforms,  the PEP can be derived from the model's posterior probability according to the Region of Practical Equivalence (ROPE) summary.  Using a two-component mixture distribution as a prior, a ROPE prior, with one component that coincides with the ROPE and the other with the region outside the ROPE, we can account for multiple comparisons.  In this prior, the mixture probabilities are random variables themselves, uniformly distributed over [0,1].  Since the mixture probabilities are shared between all the genes, the computation of their full posterior is expensive.  Instead, their MAP estimates can be derived using L-BFGS optimization.   The full posterior can then computed for each gene by using the MAP estimates in the prior.  This is the strategy that we used in our HBA-DEALS tool.

Publications:

HBA-DEALS: accurate and simultaneous identification of differential expression and splicing using hierarchical Bayesian analysis

Betacoronavirus-specific alternate splicing

The impact of biological sex on alternative splicing

Software:

HBA-DEALS