One of the most important techniques in learning about the functioning of the brain has involved examining neuronal activity in laboratory animals under varying experimental conditions. Neural information is represented and communicated through series of action potentials, or spike trains, and the central scientific issue in many studies concerns the physiological significance that should be attached to a particular neuron firing pattern in a particular part of the brain. In addition, a major relatively new effort in neurophysiology involves the use of multielectrode recording, in which responses from dozens of neurons are recorded simultaneously. Among other things, this has made possible the construction of brain-controlled robotic devices, which could benefit people whose movement has been severely impaired.

Scientific questions involving spike trains may be posed in terms of point process intensity functions, and may be answered using Bayesian methods. In my talk I will very briefly outline some of the problems that have been addressed, the progress that's been made, and the challenges to be faced as dimensionality increases.