  Latent factor models are widely used to discover and adjust for hidden
variation in modern applications. However, most methods do not fully account
for uncertainty in the latent factors, which can lead to miscalibrated
inferences such as overconfident p-values. In this article, we develop a fast
and accurate method of uncertainty quantification in generalized bilinear
models, which are a flexible extension of generalized linear models to include
latent factors as well as row covariates, column covariates, and interactions.
In particular, we introduce delta propagation, a general technique for
propagating uncertainty among model components using the delta method. Further,
we provide a rapidly converging algorithm for maximum a posteriori GBM
estimation that extends earlier methods by estimating row and column
dispersions. In simulation studies, we find that our method provides
approximately correct frequentist coverage of most parameters of interest. We
demonstrate on RNA-seq gene expression analysis and copy ratio estimation in
cancer genomics.
