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ENCN371 > Lecture 23/24 > Flashcards

Lecture 23/24 Flashcards

1
Q

aleatory uncertainty

A

natural randomness in the phenomena we are dealing with

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2
Q

epistemic uncertainty

A

inaccuracy in our understanding and our models for predicting reality

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3
Q

Three basic options

A
  • ignore the uncertainty
  • can allow for uncertainty using intuition
  • can adopt a scientific approach, use mathematical laws of probability and base decisions on internal estimates
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4
Q

politics of uncertainty

A

conceding uncertainty might be perceived as being inconsistent with being an expert

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5
Q

Type I error

A

false positive

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6
Q

Type II error

A

false negative

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7
Q

reduce type I errors

A

increase level of confidence

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8
Q

reduce type II errors

A

descriptive testing

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9
Q

s.o.n.

A

state of nature

- true value of an uncertain variable - cannot be determined with absolute confidence

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10
Q

A decision is sensitive if

A
  • one test is done and the decision is different for different test results
  • more than one test is done and the decision changes as new test results come to hand and the probability distribution for the state of nature will be updated
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11
Q

theta

A

represents the state of nature

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12
Q

z

A

represents the result of a test to obtain more information about the state of nature

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13
Q

P(theta)

A

prior probability distribution (contains prior knowledge about state of nature)

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14
Q

P(z|theta)

A

the likelihood of test result z, given the state of nature theta

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15
Q

P(theta | z)

A

posterior probability distribution (contains updated information about state of nature theta)

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16
Q

posterior analysis

A

involves calculating posterior probabilities for the state of nature, given an experiment has been done and the result is known, and then deciding what action to take

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17
Q

preposterior analysis

A

involves deciding whether an experiment should be done and which exeriment

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18
Q

four stages of preposterior analysis

A
  • the test
  • result
  • action
  • state of nature
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19
Q

Allais’ Paradox

A

lottery ticket case studies

- phenomenon is not “irrational”,but is simply the result of the way people value the possible outcomes

20
Q

Requirements for a robust numerical measure of preference

A
  • reflects the decision makers subjective preferences

- provides a scale preserving the order of expected values

21
Q

Daniel Bernoulli

A
  • assumed utility of extra wealth inversely proportional to total assets
  • proposed a scale based on the logarithm of total assets
22
Q

Buffon

A
  • proposed a scale based on the reciprocal of total assets
23
Q

Cramer

A
  • used a scale based on the square root of total assets
24
Q

von Neumann and Morgenstern

A

standard gamble

25
Q

standard gamble

A
  • enabled subjectivity to be taken into account, while fulfilling the requirement for preserving the ordering of expected values
  • based on a particular form of a decision tree, with one action leading to a certain outcome and the other to a gamble or lottery
26
Q

‘risk neutral’ person

A

bases all decisions on expected utility

27
Q

‘risk averse’ person

A

will be uncomfortable with a small p* (i.e. large probability of big loss)

28
Q

‘not risk averse’ person

A

will be comfortable with a small p* (i.e. small probability of a big win)

29
Q

Criteria for Making Decisions

A
  1. Criterion of Pure Pessimism
  2. Criterion of Pure Optimism
  3. Criterion of Regret
30
Q

Criterion of Pure Pessimism

A

(or maxi-min criterion)

  • identify for each action the minimum utility
  • choose the action with the largest minimum utility
31
Q

Criterion of Pure Optimism

A

(or maxi-max criterion)

  • identify for each action the maximum utility
  • choose the action with the largest maximum utility
32
Q

Criterion of Regret

A
  • identify the regret for each action and state of nature
  • identify for each action the maximum regret
  • choose the action with the smallest maximum regret
33
Q

reliability

A

the probability that a component (or system) will function properly

34
Q

two basic types of systems

A

series and parallel

35
Q

P[S ^ s]

A

= 1 - P[S ^ f]

36
Q

Series system

A

P[S ^ s] = P[C1 ^ s] * P[C2 ^ s] * … * P[Cn ^ s]

37
Q

Parallel systems

A
  • level of redundancy = (n-k) where k is minimum number of properly functioning components for the system to function properly
  • system fails if more than (n-k) fail
38
Q

Birnbaum

A

suggested that to maximise the improvement in network reliability (R) one should improve the link a with the highest Reliability Importance (RI)

39
Q

RI

A

Reliability Importance

RI = dR / dr(a)

40
Q

RI for series

A

RI(1) = r(2)
RI(2) = r(1)
hence if link 1 is more reliable than link 2, RI(2) > RI(1)
and should improve link 2

41
Q

RI for parallel

A

RI(1) = 1 - r(2)
RI(2) = 1 - r(1)
hence if link 1 is more reliable than link 2, RI(1) > RI(2)
and should improve length 1 - counter intuitive

42
Q

Henley and Kuamoto

A

suggested that to maximise improvement in network reliabilty, one should improve link a with highest Criticality Importance (CI)

43
Q

CI

A

Criticality Importance

CI = RI * (r / R)

44
Q

CI for two links in series

A 
CI(1) = r(2) * ( r(1) / R)
CI(2) = r(1) * ( r(2) / R)
since R = r1 * r2
CI(1) = CI(2) = 1
CI provides no help in deciding which length to strengthen
45
Q

CI for two links in parallel

A

CI(1) - C(2) = ( r(1) - r(2) ) / ( r(1) + r(2) - r(1)r(2) )

suggsts one should improve the more reliable or stronger link

ENCN371 (25 decks)

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