Reasoning Under Uncertainty Questions and Answers

Answer: C

Knowing nothing about a coin is treated differently from knowing it is fair, whereas both give a probability of one half. Whether that difference should be represented in the formalism or in a distribution over parameters is the substance of the disagreement with the Bayesian position. Interpretation, reliability and continuity are separate issues. An objection resting on what a formalism cannot distinguish is answerable either by extending it or by showing the distinction unnecessary, and both replies have been made.

Answer: D

Fuzzy logic addresses vagueness, where a man of a certain height is partly tall, rather than uncertainty about a definite fact. That is a different phenomenon from probability, and confusing the two produces a great deal of fruitless argument. Belief, second order probability and defeasibility are separate notions. Distinguishing vagueness in the predicate from uncertainty about the world is the first step in deciding which formalism a problem requires.

Answer: A

Whether a definite man of definite height counts as tall is a question about the word, not about the world, and no amount of evidence resolves it. A probability that he is tall would presuppose a sharp boundary and uncertainty about which side he falls. Arithmetic, normalisation and application area are consequences or incidental. Identifying which kind of imperfection in knowledge a problem exhibits is what selects the right formalism rather than the fashionable one.

Answer: B

Fuzzy controllers interpolate smoothly between rules stated in linguistic terms, which suits appliances and industrial control and requires no probabilistic model. Diagnosis and parameter estimation are probabilistic problems. Its success in control and its limited adoption in reasoning reflect the difference between smoothing a response surface and drawing an inference, which is a distinction worth keeping in view when a formalism is proposed for a new domain.

Answer: C

The frequentist reading defines probability by what happens in a long sequence of similar trials, which makes it hard to speak of the probability of a unique event. The Bayesian reading treats probability as belief and has no such difficulty. Model proportions and evidential support are related notions from other traditions. Knowing which interpretation is in play matters when a probability is attached to something that will happen only once.

Answer: D

An agent must have a degree of belief about this particular patient or this particular route, and no sequence of identical trials exists, so belief rather than frequency is the needed notion. Data volume and computational ease are not the argument, and priors are the distinguishing device rather than a prohibition. Choosing an interpretation because the application requires the questions it can answer, rather than on philosophical grounds, is the pragmatic position.

Answer: A

If an agent's degrees of belief violate the axioms, a set of bets can be constructed that it accepts and that loses money whatever happens. That is an argument for the axioms from consistency rather than from frequency. Convergence and prior assignment are separate results. An argument showing that violating a rule leads to a demonstrable loss, rather than merely to inelegance, is unusually persuasive.

Answer: B

The first two are correct. Exact inference is NP hard in general, and its cost depends on the network's structure through the size of the largest intermediate factor. Tree structured networks are polynomial, which is why structure matters so much. Assuming that a compact representation implies cheap inference is a natural but mistaken step, and the two properties must be established separately.

Answer: C

The four tasks differ in which state is queried and which evidence is available, and each has its own algorithm. Filtering runs online while smoothing requires the whole record, which determines which an application may use. Naming the task precisely before choosing an algorithm avoids implementing the wrong one, which is easy when the four are described loosely as tracking.

Answer: D

The first three are correct. The base rate fallacy consists in ignoring the prior rather than overweighting it, so a positive test for a rare condition is read as though the test's accuracy were the answer. Getting the direction of the error right matters, since the remedy is to attend to the base rate rather than to discount it.