Neural networks are not the only theoretical way we have to model and study nervous systems. They may not even be the most appropriate. Here I'll briefly show you another very influential approach to understanding what our brains are doing. In order to do this, I'll use the illustration of classifying primates into one of three groups (ape, australopithecine & homo) based upon two variables  brain volume and body weight. Imagine that you have a bunch of samples (living animals and known fossils) which you are using to help you classify any new fossils or skeletons found.
Neural network solutionFirst I'll show how a neural network solves the problem using the network you can download on the right.
If it isn't already done, you will need to enable iterative calculations so the network can form a feedback loop: File > Options > Formulas > enable iterative calculation > max iterations = 1 

The network will need to look at the samples in order to learn, so I've laid them out in the Excel file as shown on the left.
The first 11 samples are used for training, and the last 5 are fossils for which the species is not known. D1 and D2 are the desired outputs of the two neurons we'll use to classify the data, and they are colour coded blue and red in the two pictures below too. 
The neural network is set up as we've seen in other sections of the website. I've set the learning rate very low here  feel free to try removing a zero or two.
The thresholds are set to values that make it a bit easier for the network to learn the correct classification. We could have this as a parameter to be learnt too, but I was lazy! The pinkish box at the bottom tells us what the network thinks it's looking at. This is determined by looking at the outputs of the two neurons. 
We can also see the lines that the two neurons draw through the space of all animals.
The red neuron separates homos (blue diamonds) from australopithecines (red squares), while the blue neuron separates austroalopithecines from apes (green triangles). The black circles are the unknown fossils, but once the network has learned its classification, we can see what it thinks by looking where these dots lie with respect to the two lines. 
Bayesian classifier solutionNow let's see how a Bayesian classifier solves the problem. The program is on the right.


The whole thing is shown above. The upper part with the samples is much the same as in the neural network, except instead of the two neurons on the right, there is a group of four parameters for each genus: the average (mean) body weight (BW) and respective standard deviation, and the same two parameters for the brain volume (BV).
These parameters, along with the absolute number of samples in each genus, are used in the bottom left to calculate some probabilities of seeing an instance of any genus.
When you show the classifier an unknown sample, it calculates the probability that this sample is each of the three genera, then compares the probabilities and goes with the highest, as shown by the blue bars. Right now it's looking at a rather apelike homo.
These parameters, along with the absolute number of samples in each genus, are used in the bottom left to calculate some probabilities of seeing an instance of any genus.
When you show the classifier an unknown sample, it calculates the probability that this sample is each of the three genera, then compares the probabilities and goes with the highest, as shown by the blue bars. Right now it's looking at a rather apelike homo.
The advantage of a Bayesian classifier is that, rather than just drawing simple lines through the sample space, it finds the Gaussian distribution of each hypothesis, as shown on the right.
Imagine that the group of ape samples is lying flat on the horizontal surface of the image. The highest part of the distribution, coloured in red, is the area of sample space where the most apelike creatures are. As we move out to the yellow, then green, then blue areas, we pass animals that slowly become less apelike. At some point we will pass into an area of the sample space covered by another Gaussian  another genus. 
Below I show bird's eye views of the Gaussian distributions for each genus. If you slide over to the far right of the program, you'll find these plots. The sample space is the same for all three, but they are plotted separately because I can't find an easy way to get them on the same plot in Excel!
Anyway, you can see that the australopithecine genus has a lot of overlap with apes and a little with homos, suggesting shared features.
Anyway, you can see that the australopithecine genus has a lot of overlap with apes and a little with homos, suggesting shared features.
For you to try
Change the variables of the fossil the classifier is looking at by changing the values in cells C13 and D13.
 What values give the most typical ape, homo, austro?
 Is there an easy way to find these values from this program?
 What values confuse the classifier most? Why?
 What would happen to the Gaussian distributions if Homo habilis had a bigger brain? Try it.
 What would happen if the Gorilla's body was the same size as the Chimp's? Try it.
 Would the chance of any newly found fossil being an Australopithecine change if we had more samples of Australopithecines?