Cells send and receive signals through pathways that have been defined in great detail biochemically, and it is often presumed that the signals convey only level information. Cell signaling in the presence of noise is extensively studied but only rarely is the speed required to make a decision considered. However, in the immune system, rapidly developing embryos, and cellular response to stress, fast and accurate actions are required. Statistical theory under the rubric of exploit-explore quantifies trade-offs between decision speed and accuracy and supplies rigorous performance bounds and algorithms that realize them. We show that common protein phosphorylation networks can implement optimal decision theory algorithms and speculate that the ubiquitous chemical modifications to receptors during signaling actually perform analog computations. We quantify performance trade-offs when the cellular system has incomplete knowledge of the data model. For the problem of sensing the time when the composition of a ligand mixture changes, we find a nonanalytic dependence on relative concentrations and specify the number of parameters needed for near-optimal performance and how to adjust them. The algorithms specify the minimal computation that has to take place on a single receptor before the information is pooled across the cell.