2.6 Robust inferences

One objection we may have with model_g is that we are assuming a Normal distribution, but we have two data points away from the bulk of the data. By using a Normal distribution for the likelihood, we are indirectly assuming that we are not expecting to see a lot of data points far away from the bulk. Figure 2.13 shows the result of combining these assumptions with the data. Since the tails of the Normal distribution fall quickly as we move away from the mean, the Normal distribution (at least an anthropomorphized one) is surprised by seeing those two points and reacts in two ways, moving its mean towards those points and increasing its standard deviation. Another intuitive way of interpreting this is by saying that those points have an excessive weight in determining the parameters of the Normal distribution.

So, what can we do? One option is to check for errors in the data. If we retrace our steps we may find an error in the code while cleaning or preprocessing...