In real data analysesd simulation studies we find our methods often lead to dramatic decreases in false positves (FDR can drop from >75% to a nominal 5%) while simultaneously maintaining or improving statistical power.

New results soon to be released:

We have developed specialized PIMs that account for uncertainty in sparsity assumptions. 6 datasets with ground truth, comparing against 8 methods. When our assumptions hold (first 4 datasets) our methods do well. When violated (last two) they fail gracefully.

www.biorxiv.org/content/10.1...

Here we benchmark against 5 common methods using 2 real datasets.

www.biorxiv.org/content/10.1... (in revision at Genome Biology)

3 real datasets (1 more coming in revision), compared against 5 competing methods (ALDEx2, BayeSeq, DESeq2, edgeR, limma).

Not everyone likes Bayesian models. Recently we Developed Frequentist analogues of these methods which are easier to specify and more robust to model misspecification (red and blue line below).
www.biorxiv.org/content/10.1...

In collaboration with @gbgloor, Bayesian PIMs are now part of ALDEx2. We find these methods are universally better and recommend their (over prior defaults) in all practical scenarios! In the below plot, scale methods are Bayesian PIMs in ALDEx2.
www.biorxiv.org/content/10.1...

We have also showed these issues occur in gene and microbe set enrichment analyses journals.plos.org/ploscompbiol....
Even slight errors in normalization assumptions about scale (epsilon not equal to zero in this plot) can invalidate conclusions drawn from current methods.

In multiple papers (example below) we show current methods can lead to massively elevated Type-I and Type-II error rates (e.g., >70%).
From www.biorxiv.org/content/10.1... (in review at Genome Biology).