Probability

CSC 261 - Artificial Intelligence - Weinman

1. Jaynes gives several desiderata (I, II, IIIa, IIIb,IIIc) for a theory of plausible reasoning. Which of these do you feel best motivates the product rule? Briefly (3-5 sentences) explain your choice.
2. The last rule of the derivation at the start of Section 13.2.3 (p. 488), which may be re-arranged as
   

   1=P(a)+P(¬a)

   is often called the sum rule. Which of Jaynes's desiderata do you feel best motivates the sum rule? (Hint: Consider what the rule says must happen to the plausibility of ¬a when the plausibility of a changes.) Briefly explain your choice.
3. Give an example from your own everyday experience in colloquial "reasoning under uncertainty" that is analogous to either marginalization or conditioning. In particular, you should identify
   • what variable or proposition you are trying to assess your belief about (the query),
   • what other (unknown) variable(s) or proposition(s) were logically connected to the query but eliminated (marginalized), and
   • some qualitative properties of
     • the joint probability distribution (in the case of marginalization) or
     • the conditional and prior distributions (in the case of conditioning).
4. Select the sentence or short passage (no more than three sentences, please) that you find most provocative or surprising from the reading in Jaynes. Briefly explain why you selected this particular sentence or short passage.