Reasoning Under Uncertainty Questions and Answers

Answer: A

Probability, evidence theory and certainty factors all address uncertainty about definite facts. Fuzzy logic addresses vagueness in the predicates themselves, which is a different phenomenon. Confusing the two leads to arguments in which each side is discussing a different problem. Sorting formalisms by the kind of imperfection they address, rather than by the numbers they manipulate, is what makes the comparison meaningful. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Answer: B

Both are true and the second is the reason. A joint over twenty binary variables needs a million numbers, while a sparse network needs a few dozen, and the reduction comes entirely from the conditional independences the structure asserts. Inference remains hard in the worst case, so representation and computation must be considered separately. That a structural assumption converts an impossible representation into a routine one is the central result of the topic.

Answer: C

A random variable ranges over a set of possible values with a probability attached to each, and the uncertainty lies in the agent's knowledge rather than in the world necessarily. Random choice, unpredictable change and measurement error are different notions. Recognising that the randomness describes a state of information, rather than a property of the thing described, is what makes the Bayesian reading coherent.

Answer: D

The distribution gives a non-negative number to each value with the numbers summing to one, which is the complete description of the agent's belief about that variable. Averages, ranges and conversions are different notions. Insisting on the normalisation condition is what makes the numbers interpretable as probabilities rather than as arbitrary scores.

Answer: A

The joint assigns a probability to each complete assignment, so every question about the variables can be answered from it by summing appropriately. Its size is exponential, which is why factorisation matters. Sums of variables, shared beliefs and averages are different notions. That the joint answers everything and cannot be stored is the tension the whole topic exists to resolve.

Answer: B

Summing out the unwanted variables leaves the distribution over those that remain, which is how any query is answered from a joint. It is the operation variable elimination reorganises to avoid repeated work. Discarding, ignoring and mode selection are different operations. Knowing that every probabilistic query reduces to summing and normalising is what makes the algorithms comprehensible as optimisations of an obvious procedure. Naming the cost of a choice alongside its benefit is what turns a fact into a design decision.

Answer: C

Conditioning discards the outcomes inconsistent with what was observed and renormalises the rest, which is exactly what Bayes' rule computes. Multiplication by the evidence probability would be division, removal loses information and prior adjustment is a different operation. Understanding conditioning as restriction plus renormalisation makes the rule intuitive rather than a formula to be memorised.

Answer: D

The rule writes a joint as a product of conditionals, each variable given those before it in an arbitrary ordering, and choosing an ordering in which each variable depends on few predecessors gives a Bayesian network. Event chains, sequential conditioning and transitivity are different notions. That the factorisation is always available, and that structure comes from choosing a good order, is the derivation of the network representation in one step.

Answer: A

The chain rule always gives a factorisation, and conditional independence lets each factor drop the predecessors that add nothing, leaving only the parents. The saving comes entirely from those dropped conditionings. Exactness is unaffected by the ordering, repetition is not required and estimation is a separate matter. Deriving the representation from an identity plus an assumption, rather than positing it, shows exactly where its power comes from.

Answer: B

Listing causes before effects usually lets each node depend on few predecessors, whereas the reverse ordering forces dense connections that encode the same distribution far less compactly. Every ordering is exact, and observation is unrelated. That the same distribution may have a sparse or a dense representation, according to how it is written, is why structure learning and expert elicitation both begin by seeking the causal direction. Most errors here come from carrying a result across from a neighbouring case where it does not hold.