DescriptionCross-selective receptor arrays coupled with higher-order neural processing can be seen in naturally occurring olfactory systems, where a large number and variety of analytes can be detected, distinguished, even quantified using relatively few receptors and clever combinatorial odor decoding. This strategy has been imitated in artificial sensor array systems that are paired with computational signal-processing tools in diverse applications that range from vintage wine year discrimination to disease diagnosis. However, the complexity of receptor response patterns to even a single analyte, coupled with non-linearity of response to mixtures of analytes, makes quantitative inference of individual compound concentrations within mixtures a challenging task. In this work, I show how output from two distinct types of sensor arrays, each combined with Bayesian analysis, can be used to predict component concentrations in complex mixtures. In the first case, the array consists of four engineered G-protein-coupled receptors used for deciphering mixtures of highly related sugar nucleotides. We employ a biophysical model that explicitly takes receptor-ligand interactions into account in order to quantify mixture constituents. Furthermore, we develop a universal metric of receptor array performance, and use it to study the fundamental limits imposed on the accuracy of ligand recognition by the physics and biology of receptor-ligand interactions. This provides design guidelines for sensor arrays optimized for mixture analysis. Antagonistic receptor response, well-known to play an important role in biological systems, proves to be essential for precise recognition of mixture components. The second array consists of a mixed-potential electrochemical sensor operating under different applied bias currents to monitor gas mixtures in diesel engine exhaust. Here, the sensitivity and selectivity of a device is tuned by current application, thus a single sensor serves as an entire array when operated under multiple conditions. Both a linear and non-linear model are used to quantify ammonia gas in the presence of propylene interference. While more data-intensive, the nonlinear model captures cross-interference between analytes and yields more accurate predictions. Our Bayesian methodology is easily generalized to other `artificial nose' applications by the inclusion of additional models.