Reasoning Under Uncertainty Questions and Answers

Answer: A

Exact inference is NP-hard in general, though polytrees admit linear-time inference, so the difficulty lives in the loops. Storage, evidence handling and numerical error are real engineering concerns but are not the source of the complexity result. Knowing that the hardness is structural, and that a whole class of networks escapes it, is what makes approximate methods a considered choice rather than a retreat.

Answer: B

Rejection sampling draws complete samples from the prior and throws away those inconsistent with the evidence, estimating the query from what survives. It is correct and hopelessly wasteful when the evidence is unlikely, since almost every sample is discarded. Thresholds, unassigned parents and burn-in belong to other methods. Its inefficiency is precisely the problem likelihood weighting sets out to fix.

Answer: C

Evidence variables are clamped rather than sampled, and each sample carries the product of the evidence likelihoods as its weight, so no sample is wasted. Performance still degrades when the evidence sits far downstream. Variable weighting, importance regions and relaxed evidence are different ideas. Understanding the weight as an importance-sampling correction explains both why it works and where it fails.

Answer: D

Gibbs walks a Markov chain over complete assignments, resampling one non-evidence variable at a time from its Markov blanket, and the chain's stationary distribution is the posterior. Direct sampling, exact truncation and mode search are different things. The cost is that consecutive samples are correlated and the chain needs time to mix, which is why burn-in and convergence checks belong to the method.

Answer: A

The estimated probabilities are badly calibrated, often near zero or one, but the class with the largest score is frequently still the right one, and classification needs only the argmax. Real features are rarely independent, the errors do not cancel exactly, and the prior does not repair them. Separating calibration from discrimination is the general point, and it recurs whenever a model is judged by accuracy alone.

Answer: B

Utility assigns a number to each outcome so that preferences are respected, and rational choice maximises expected utility. It is defined only up to a positive affine transformation, so absolute values carry no meaning. Evidence value, success probability and cost are different quantities. The representation theorem behind it, deriving utility from a handful of preference axioms, is what stops the number being arbitrary.

Answer: C

A concave utility means each additional unit of money is worth less than the last, so a sure amount is preferred to a gamble of equal expected value. The preference emerges from the shape of the curve, with no change to probabilities and no separate penalty. Variance preference is a symptom rather than the representation. That the same MEU rule covers cautious and reckless agents alike is what makes the framework general. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Answer: D

The certainty equivalent is the sure sum whose utility equals the gamble's expected utility, and it falls below the expected value for a risk-averse agent. The gap is the insurance premium. Expected value, avoidance payment and utility rescaling are related but distinct. Computing it once for a concave curve makes the whole vocabulary of risk premiums fall into place.

Answer: A

The denominator is the probability of the evidence summed over every hypothesis, and it merely rescales so the posteriors sum to one. Because it is common to all hypotheses it can be ignored when only the ranking matters, which is why the proportional form of the rule is so often used. Priors, maximum likelihoods and hypothesis counts are different quantities. Treating the constant as bookkeeping rather than as content removes most of the algebra from the rule and leaves the idea visible.

Answer: B

The ratio divides the two likelihoods and multiplies the prior odds to give the posterior odds, so it is exactly the weight of evidence. It says nothing about the priors and nothing about how many observations are needed. Working in odds rather than probabilities makes sequential updating a simple product, which is why diagnostic reasoning is usually taught this way. Recognising the ratio as the only part of the evidence that matters is the practical lesson.