Reasoning Under Uncertainty Questions and Answers

Q: Which situation defeats the Kalman filter's assumptions?

A Gaussian has one mode, so a belief that is genuinely split between two possibilities cannot be represented at all, which is the classic case for particle filtering. High dimension is expensive but tractable, irregular timing is handled by adjusting the transition, and large noise merely widens the covariance. Identifying the failure as representational rather than computational is what makes the choice of filter principled.

Q: Which reasoning pattern does probability handle that logic handles badly?

Probabilistic belief rises and falls with evidence, so a conclusion drawn now can be withdrawn later without any special machinery, whereas monotonic logic needs default rules and truth maintenance to imitate it. Large premise sets, quantification and premise ordering are handled by logic perfectly well. This non-monotonic behaviour, with explaining away as its sharpest example, is the historical reason probability displaced its rivals here.

101.

Which situation defeats the Kalman filter's assumptions?

A.A multimodal belief about the state
B.A state space with a large number of separate dimensions
C.Observations arriving at irregular intervals of time
D.Noise whose variance is larger than expected at the outset

Answer: A

A Gaussian has one mode, so a belief that is genuinely split between two possibilities cannot be represented at all, which is the classic case for particle filtering. High dimension is expensive but tractable, irregular timing is handled by adjusting the transition, and large noise merely widens the covariance. Identifying the failure as representational rather than computational is what makes the choice of filter principled.

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102.

Which reasoning pattern does probability handle that logic handles badly?

A.Conclusions that depend on the order the premises are presented
B.Conclusions that later evidence can retract
C.Conclusions that follow from a very large number of premises
D.Conclusions about individuals drawn from statements about classes

Answer: B

Probabilistic belief rises and falls with evidence, so a conclusion drawn now can be withdrawn later without any special machinery, whereas monotonic logic needs default rules and truth maintenance to imitate it. Large premise sets, quantification and premise ordering are handled by logic perfectly well. This non-monotonic behaviour, with explaining away as its sharpest example, is the historical reason probability displaced its rivals here.

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