We review some of our recent results on establishing a neuronal decision theory and spiking ICA (independent component analysis). For neuronal decision theory, we show that the discrimination capacity of a model neuron is a decreasing function of inhibitory inputs. Increasing the output variability of neuron efferent firings implies an improvement of neuron discrimination capacity. For the two most interesting cases, with or without inhibitory inputs, the critical discrimination capacity is exactly given. For spiking ICA, by a simple combination of the Informax principle and the input-output relationship of a spiking neuron, we first develop a learning rule. By applying the learning rule to linear mixture of signals, we demonstrate that spiking neuron network can accomplish ICA tasks.