In this article, we propose differentially private methods for hypothesis testing, model averaging, and model selection for normal linear models. We propose Bayesian methods based on mixtures of $g$-priors and non-Bayesian methods based on likelihood-ratio statistics and information criteria. The procedures are asymptotically consistent and straightforward to implement with existing software. We focus on practical issues such as adjusting critical values so that hypothesis tests have adequate type I error rates and quantifying the uncertainty introduced by the privacy-ensuring mechanisms.

MOTIVATION: Designing an RNA-seq study depends critically on its specific goals, technology and underlying biology, which renders general guidelines inadequate. We propose a Bayesian framework to customize experiments so that goals can be attained and resources are not wasted, with a focus on alternative splicing. RESULTS: We studied how read length, sequencing depth, library preparation and the number of replicates affects cost-effectiveness of single-sample and group comparison studies. Optimal settings varied strongly according to the target organism or tissue (potential 50-500% cost cuts) and, interestingly, short reads outperformed long reads for standard analyses. Our framework learns key characteristics for study design from the data, and predicts if and how to continue experimentation. These predictions matched several follow-up experimental datasets that were used for validation. We provide default pipelines, but the framework can be combined with other data analysis methods and can help assess their relative merits. AVAILABILITY AND IMPLEMENTATION: casper package at www.bioconductor.org/packages/release/bioc/html/casper.html, Supplementary Manual by typing casperDesign() at the R prompt. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.