Click "Know Location" to set the prior distribution to a point mass at a random location. Next, "Observe Door" and "No Light". What happens? Give an intuitive reason for your observation. How might this be a problem in real applications, and how might we solve it?
- The belief does not change. This is because the prior places 0 probability on all positions except one, effectively ruling out all other possibilities as impossible. This could be a problem if our prior was false, since no amount of evidence would correct our belief; we would simply conclude that the measurements are wrong. To remedy this, we can put a small but non-zero prior on the other locations, to account for the possibility that our initial guess is wrong. This is analoguous to putting pseudocounts (see for example, the decision tree exercise). We should take care that the conditional probabilities in our dynamics and sensing model do not place zero probabilities on rare but possible outcomes.