Write a brief (~1.5 page) essay in answer to each of the following questions.
1. Bayes' theorem can be written:
P(Cause|Effect) = (P(Effect|Cause) * P(Cause)) / P(Effect)
The meaning of P(Cause|Effect) is the probability of a cause being true given that we have seen some effect.
In other words: the idea is that if we see some "effect" (such as a friend with a suntan) we might hypothesize some cause (such as the possibility that the friend just took a trip to Florida).
Give an example of some instance in which you might employ "Bayesian reasoning" in your everyday experience, and make some estimate of the appropriate probability values on the right side of the equation above.
2. In the Kahneman and Tversky paper, several problematic heuristics are mentioned that occasionally lead to mistaken judgments: representativeness, availability, and anchoring. For at least two of these, give a brief definition of the idea and describe an instance in your experience (other than those in the article) in which the heuristic might be either especially effective or mistaken.
3. In class, we saw a variety of ideas about how different aspects of vision could be treated as computational problems. Consider the processes of (for instance) edge detection, depth perception, and object recognition as discussed in the readings and in class from the standpoint of optical illusions. In other words, what sorts of illusions highlight the properties (or potential "weak spots") in our visual algorithms?