Aberrant splicing is a major cause of rare diseases. However, its prediction from genome sequence alone remains in most cases inconclusive. Recently, RNA sequencing has proven to be an effective complementary avenue to detect aberrant splicing. Here, we develop FRASER, an algorithm to detect aberrant splicing from RNA sequencing data. Unlike existing methods, FRASER captures not only alternative splicing but also intron retention events. This typically doubles the number of detected aberrant events and identified a pathogenic intron retention in MCOLN1 causing mucolipidosis. FRASER automatically controls for latent confounders, which are widespread and affect sensitivity substantially. Moreover, FRASER is based on a count distribution and multiple testing correction, thus reducing the number of calls by two orders of magnitude over commonly applied z score cutoffs, with a minor loss of sensitivity. Applying FRASER to rare disease diagnostics is demonstrated by reprioritizing a pathogenic aberrant exon truncation in TAZ from a published dataset. FRASER is easy to use and freely available.