  Peptide microarrays have emerged as a powerful technology in immunoproteomics
as they provide a tool to measure the abundance of different antibodies in
patient serum samples. The high dimensionality and small sample size of many
experiments challenge conventional statistical approaches, including those
aiming to control the false discovery rate (FDR). Motivated by limitations in
reproducibility and power of current methods, we advance an empirical Bayesian
tool that computes local false discovery rate statistics and local false sign
rate statistics when provided with data on estimated effects and estimated
standard errors from all the measured peptides. As the name suggests, the
\verb+MixTwice+ tool involves the estimation of two mixing distributions, one
on underlying effects and one on underlying variance parameters. Constrained
optimization techniques provide for model fitting of mixing distributions under
weak shape constraints (unimodality of the effect distribution). Numerical
experiments show that \verb+MixTwice+ can accurately estimate generative
parameters and powerfully identify non-null peptides. In a peptide array study
of rheumatoid arthritis (RA), \verb+MixTwice+ recovers meaningful peptide
markers in one case where the signal is weak, and has strong reproducibility
properties in one case where the signal is strong. \verb+MixTwice+ is available
as an R software package.
\href{https://github.com/wiscstatman/MixTwice}{https://github.com/wiscstatman/MixTwice}
