High-throughput technologies, including gene-expression microarrays, hold great promise for the systems-level study of biological processes. Yet, challenges remain in comparing microarray data from different sources and extracting information about low-abundance transcripts. We demonstrate that these difficulties arise from limitations in the modeling of the data. We propose a physically motivated approach for estimating gene-expression levels from microarray data, an approach neglected in the microarray literature. We separately model the noises specific to sample amplification, hybridization, and fluorescence detection, combining these into a parsimonious description of the variability sources in a microarray experiment. We find that our model produces estimates of gene expression that are reproducible and unbiased. While the details of our model are specific to gene-expression microarrays, we argue that the physically grounded modeling approach we pursue is broadly applicable to other molecular biology technologies.