Neural decoding is the process of attempting to infer features of a stimulus or other external variable from measurements of neurons' activity. The idea is that the neuronal response is encoding information about the inputs to the brain. If one understood how the information is encoded, then one might be able to go backward and make conclusions about these inputs by analyzing patterns of neuronal activity. This backward inference is at the heart of decoding. Since decoding is an attempt to interpret what the brain's activity means, we can whimsically refer to it as mind reading.
For this project, we will analyze a highly idealized scenario so that we can frame the decoding problem in terms of simple probability. We will starting by imagining that we are measuring whether or not a single neuron in a rat's brain spikes once in one short time window. From this single measurement, we'll attempt to infer the rat's location. (In a more realistic setting, we should simultaneously measure the spiking activity from many tens of neurons over a period of many seconds, obtaining thousands of spikes from which to decode the rat's location.)
The overarching questions of this project are:
What types of conclusions about the rat's location can we make from just observing a neuron's spikes?
What properties of the neuronal spiking enhance or detract from the decoding?
Imagine that a rat is exploring two adjacent rooms while the response of a single neuron is being measured. From initial testing where you both observe the rat and measure the neuron, you discover two things. First the rat spends twice as much time in room A than in room B. Second, when you measure to determine if the neuron spiked in a 10 ms window, the likelihood of measuring a spike depends on the room. When the rat is in room A, you measure a spike about 10% of the time. On the other hand, when the rat is in room B, you measure a spike about 2% of the time.