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Detecting genetic variants associated with traits (quantitative trait loci, QTL) requires genotyped study individuals. Here we describe BaseQTL, a Bayesian method that exploits allele-specific expression to map molecular QTL from sequencing reads (eQTL for gene expression) even when no genotypes are available. When used with genotypes to map eQTL, BaseQTL has lower error rates and increased power compared with existing QTL mapping methods. Running without genotypes limits how many tests can be performed, but due to the proximity of QTL v